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This article presents a systematic approach to nonlinear state‐feedback control design that has three main advantages: (i) it ensures exponential stability and ℒ2$$ {\mathcal{L}}_2 $$‐gain performance with respect to a user‐defined set of reference trajectories, (ii) it provides constructive conditions based on convex optimization and a path‐integral‐based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter‐varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and ℒ2$$ {\mathcal{L}}_2 $$‐gain performance for all trajectories of the targeted reference behavior. We show that the proposed methodology is a unified generalization of the two distinct categories of linear‐parameter‐varying (LPV) state‐feedback control approaches: global and local methods. Moreover, it provides rigorous stability and performance guarantees as a method for nonlinear tracking control, while such properties are not guaranteed for tracking control using standard LPV approaches. Code is available at https://github.com/ruigangwang7/VCCM. [ABSTRACT FROM AUTHOR]

The stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays. [ABSTRACT FROM AUTHOR]

Many practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system. [ABSTRACT FROM AUTHOR]

The problem of event‐triggered control (ETC) of stochastic nonlinear delayed systems with state quantization is investigated. In order to reduce the communication burden and computational cost, an ETC mechanism and state quantization are introduced in the control scheme. Two configurations are considered to investigate their interaction: quantization before event‐trigger (QE) and quantization after event‐trigger (EQ), respectively. Based on this, a static event‐triggered mechanism (ETM) is designed while avoiding the Zeno phenomenon. The system allows known input‐to‐state stability (ISS) control law, followed by utilizing the Halanay inequality to achieve stabilization. In both configurations, the stabilization of the closed‐loop system is guaranteed. We show that communication times can be reduced by adjusting parameters and selecting the suitable configuration. Moreover, to further enhance resource conservation, we illustrate the feasibility of dynamic ETMs in this framework. Numerical simulation results validate the effectiveness of the proposed ETC schemes. [ABSTRACT FROM AUTHOR]

The existing researches mainly focused on control issues of systems with constant powers. In practical engineering, it shows that some dynamic systems have time‐varying powers, which result in the inapplicability of many reported methods. Besides, nonlinear systems constantly suffer from uncertain dynamics. This article discusses the control issue of systems which possess uncertain dynamics and time‐varying powers. By introducing a new Lyapunov function which contains quadratic components and high‐order components and raising a novel recursive design strategy, we successfully design a semi‐global practical finite time controller which allows uncertain dynamics and larger range of system powers. Numerical and practical examples show that the presented strategy is valid. [ABSTRACT FROM AUTHOR]

This article addresses the stabilization problem of continuous‐time Markovian jump systems (MJSs). Because of both switching and state signals sampled, a novel system with an exponential matrix characterizing the sampling effects is developed. It is used to be an auxiliary system and plays important roles in system analysis and synthesis. Sufficient stabilization conditions are presented and fully consider the sampling rate. The applications of established methods and results are applied to networked control in the presence of denial‐of‐service (DoS). The frequency and duration of DoS attacks ensuring stability of the closed‐loop system are characterized. Meanwhile, more special situations about particular transition rate matrix, sampling logic and improved mode‐dependent controller are considered respectively. The analysis results are significant and bring an important method to study the control for MJSs with sampled switching and state signals. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study. [ABSTRACT FROM AUTHOR]

The original purpose of this article is to tackle the stabilizing controller design for linear parameter varying positive systems with multiple delays, in which the considered delays are time‐invariant. The proposed control strategy consists of a parameter varying state‐feedback controller. A complete solution to the design problem is proposed by utilizing a Lyapunov approach. In order to decrease the conservativeness of the controller design, we define a slack variable to prevent the multiplication of the Lyapunov matrices with the system matrices. Moreover, the slack variable is considered as a parameter varying matrix. Finally, the criteria are transformed into linear matrix inequalities. Therefore, sufficient conditions stabilize the closed‐loop system and preserve the positive property. A special case for the mentioned system is the deep brain stimulation system used in the area of Parkinson's treatment. It enables neuroscientists to control abnormal brain activity by implanting electrodes that generate electrical impulses. This system is provided as a practical example to guarantee the effectiveness of the obtained outcomes. [ABSTRACT FROM AUTHOR]

This article addresses the asymptotical mean square stability problem of continuous‐time delayed Markovian jump systems (MJSs). Different from the existing delayed MJS models, time‐varying delays are contained in not only system state but also switching signal and could lead to great difficulties. An auxiliary system approach is developed to handle the difficulties, in which the traditionally delayed state and a new delayed exponential matrix are both involved. Based on the established model, sufficient stability conditions with solvable forms are given by using a Lyapunov function approach and some novel techniques. More extensions about an MJS under sampled switching and state signals are further considered, and so does the stabilization problem. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study. [ABSTRACT FROM AUTHOR]

In this article, the stabilization is addressed for the continuous‐time nonhomogeneous nonlinear Markovian jump system (MJS) with parameter uncertainty and stochastic disturbance via sliding mode control (SMC) technique. By using a piecewise homogeneous Markov chain to describe its time‐varying characteristics, the considered nonhomogeneous MJS is established by two kinds of piecewise homogeneous MJSs. After that, an integral sliding mode function is constructed. Then, by applying the SMC theory, two control schemes are proposed to force the states of the piecewise homogeneous MJSs onto the designed sliding surface. Sufficient conditions are given to assure the stochastic stability of the sliding mode dynamics. In addition, the reachability of the system states under the developed SMC law is discussed via Lyapunov stability theory. Lastly, some simulation results are provided to show the effectiveness of the presented SMC methods. [ABSTRACT FROM AUTHOR]

The adaptive control issue of uncertain nonlinear system which has complicated polynomial growing condition is studied. Utilizing the dynamic‐gain transformation, we transform the considered system into the time‐varying system. By using a recursively design for its nominal system, a controller is skillfully constructed first. Subsequently, for the original system, by flexibly utilizing the dynamic gain and presenting an adaptive homogeneous domination method, a new time‐varying adaptive controller is successfully obtained to ensure that the equilibrium point is globally asymptotically stable. An extended robust adaptive controller is also provided. Finally, we discuss two examples to verify the proposed approach. [ABSTRACT FROM AUTHOR]

This article focuses on the robust H∞ observer‐based controller (H∞‐ROBC) for Uncertain Fractional‐Order Systems with Time‐Varying‐Delay (DU‐FOS‐TVD). First, the existence conditions of H∞‐ROBC are given. Then, based on the diffusive representation of the fractional‐order derivative and the indirect Lyapunov approach, a new sufficient condition is obtained and presented as a convex optimization problem with a Linear Matrix Inequality (LMI) constraint, which guarantees the robust stability of the estimation errors and the stabilization of the DU‐FOS‐TVD simultaneously. All observer matrices gains and control laws can be computed by solving the given LMI. A Numerical example is given to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This article considers the stabilization problem of continuous‐time semi‐Markovian jump systems. A kind of stochastically scheduled controller is proposed to realize the aim. It could also suffer a case that no controller is added to subsystems during some time slices. Based on a Lyapunov approach, sufficient conditions for such a controller are presented with LMI forms. Both sojourn times of jump signal and distribution properties of stochastic scheduling are involved and have positive roles in getting better performances. Two special cases about mode‐dependent and mode‐independent controllers are directly obtained. A practical example is given to verify the effectiveness and superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

Summary: In this article, the exponential stabilization for a class of switched nonlinear delayed systems is addressed via aperiodic sampled‐data control with asynchronous switching. A new type of looped multiple Lyapunov‐Krasovskii functionals (LKFs) is developed, which depend both on the system modes and on the controller modes. Moreover, the constructed looped LKFs are discontinuous and relax restrictions on positive definiteness that is only required at the sampling instants and at the switching instants of system modes. Based on the looped multiple LKFs, the average dwell time approach, and some estimation techniques, a less conservative stability criterion is derived to ensure the exponential stability of the closed‐loop system. Furthermore, by decoupling the matrix inequalities in the stability criterion, a LMI‐based design algorithm for the control gains is developed, which gets further refined and becomes more flexible due to the introduction of the two adjustable parameters. Two simulation examples are finally provided to validate the effectiveness and superiority of the proposed functionals and the obtained results over some existing ones. [ABSTRACT FROM AUTHOR]

Summary: In this article, a fuzzy boundary geometric controller that stabilizes a class of nonlinear distributed parameter systems (DPSs) is proposed. The design procedure relies on the use of Takagi‐Sugeno (T‐S) type fuzzy partial differential equation (PDE) model, which approximates the dynamical behavior of the nonlinear DPS. The T‐S fuzzy PDE model is constructed through "fuzzy blending" of local linear PDE models of infinite characteristic indexes. This is a challenging task in the design procedure of fuzzy PDE model‐based boundary controller in the framework of the well‐established geometric control theory. To overcome this constraint, it is proposed in this article to resort to the concept of extended operator in order to transform the T‐S fuzzy PDE model with boundary control to an equivalent fuzzy PDE model with punctual control and finite characteristic index. Based on the developed fuzzy model, a fuzzy boundary geometric controller is derived and sufficient conditions of exponential stability of the resulting closed‐loop system are established by employing the Lyapunov direct method. The stabilizing performance of the proposed fuzzy PDE model‐based boundary geometric controller is evaluated on benchmark control problems and compared with other existing control methods via numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: The aim of this article is to design a suitable strength function g(t,x,r(t)) such that the Wiener noise g(t,x(t),r(t))dw(t) either stabilizes or destabilizes a given nonlinear and time‐varying hybrid system x˙(t)=f(t,x(t),r(t)). To this end, the basic properties, including the existence and uniqueness of the local and global solutions and the nonzero property of solutions of the nonlinear and time‐varying hybrid stochastic systems, are first investigated as the theoretical basis of the article. Second, two theorems and the corresponding corollaries on the stability and instability of the hybrid stochastic systems are established. Third, the design method for the noise strength g(t,x,r(t)) is then proposed based on the established theorems. We also point out that the Markov jump r(t) may have a stabilizing (respectively, destabilizing) effect when we design the noise strength g(t,x,r(t)) so that the introduced noise g(t,x(t),r(t))dw(t) stabilizes (respectively, destabilizes) the corresponding hybrid system. Finally, we illustrate our method using two examples. Compared with the existing literature, our method is suitable for a wider class of nonlinear and time‐varying systems with weaker conditions than quasi‐linear systems. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any ϵi∈(0,ϵ‾i] with positive bound ϵ‾i predefined. First, stability conditions expressed ϵi‐free but involving its bound are developed by constructing an ϵi‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods. [ABSTRACT FROM AUTHOR]

Summary: In this work, we investigate stabilization and optimization issues for a class of multimodule impulsive switched linear systems. First, we establish a necessary and sufficient criterion on asymptotic stabilizability via a pathwise state‐feedback scheme, which achieves the merits of both time‐driven and state‐feedback mechanisms. Then, we present an impulse/switching instant optimization problem that usually arises in finite‐horizon optimal control. To reduce the computational burden, we propose a novel method via developing efficiently computable expressions for the cost function, the gradient vector, and the Hessian matrix. Next, we design a second‐order optimization algorithm searching for the optimal impulse/switching instants. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: In this paper we propose a new design paradigm, which employs a postprocessing internal model unit, to approach the problem of output regulation for a class of multivariable minimum‐phase nonlinear systems possessing a partial normal form. Contrary to previous approaches, the proposed regulator handles control inputs of dimension larger than the number of regulated variables, provided that a controllability assumption holds, and can employ additional measurements that need not to vanish at the ideal error‐zeroing steady state, but that can be useful for stabilization purposes or to fulfill the minimum‐phase requirement. Conditions for practical and asymptotic output regulation are given, underlying how in postprocessing schemes the design of internal models is necessarily intertwined with that of the stabilizer. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the stabilization problem of stochastic Markovian switching systems on networks with multilinks and time‐varying delays (SMNMT) is investigated via aperiodically intermittent control. At first, a new differential inequality is established for SMNMT, which relaxes the conditions of time‐varying delays compared with existing literature. Different from previous approaches of studying multilinks systems, new differential inequality technique combined with graph theory and Lyapunov method is adopted, based on which two types of sufficient conditions are derived to ensure the stability of SMNMT. The topological structure of multilinks systems on networks, stochastic perturbation, the transition rate of Markov chain, and intermittent control has a great impact on these developed conditions. The theoretical results are applied to stochastic Markovian switching oscillators networks with multilinks (SMONM), and a stabilization criterion of SMONM is derived as well. Finally, a numerical example is shown to illustrate the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

Summary: The wide class of nonlinear stationary systems of ordinary differential equations taking into account restrictions on control and external perturbation is considered. An algorithm for constructing a discrete control function that guarantees the transfer of the systems from the initial state to the origin and an arbitrary neighborhood of the origin is proposed. A constructive sufficient condition of the Kalman type, in which the specified translation is possible, is obtained. The problem of robot‐manipulator control is considered and its numerical simulation is carried out. [ABSTRACT FROM AUTHOR]

Summary: This paper aims to stabilize a scalar continuous‐time linear system that transmits its feedback information through a digital communication network. The finite bit rate of the feedback network plays a critical role in the input‐to‐state stability of that system. Stabilizing bit rate conditions depend on not only the system matrix but also the uncertainty of the system matrix and the unknown clock offset between the transmitter (sensor) and the receiver (controller). Compared with the current literature, this paper can handle the system matrix uncertainty and clock offset through implementing an event‐triggered sampling strategy and derive stabilizing conditions that require lower bit rates than those of periodic sampling strategies. Such bit rate saving mainly comes from the fact that our event‐triggered strategy can extract state information from the receive time instants of feedback packets without any extra communication cost. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a robust neural network–based control scheme to deal with the problem of tracking and stabilization simultaneously for a wheeled mobile robot subject to parametric uncertainties, external disturbances, and input saturation. At first, a new error‐state transformation scheme is designed by introducing some auxiliary variables as an additional virtual control signals to reduce the adverse effect caused by the underactuation. These variables can change their structures for different desired trajectories to be tracked. Then, a robust control law is proposed combining with a kinematic controller and a dynamic controller, while a three‐layer neural network system is applied to approximate model uncertainties. Stability analysis via the Lyapunov theory shows that the proposed controller can make tracking errors converge to bounded neighborhoods of the origin. Finally, some simulation results are illustrated to verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: We study two broad classes of nonlinear time‐varying continuous‐time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance affects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the efficacy of our methods. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper establishes new criteria for stochastic suppression and stabilization of hybrid functional differential systemswith general 1-sided polynomial growth condition. For an unstable nonlinear hybrid functional differential system with general 1-sided polynomial growth condition, 2 independent Brownian noise processes are used to perturb the system into the stochastic hybrid differential system. Theoretical analysis shows that one of the nonlinear diffusion termsmay suppress the explosive solution of deterministic system, and the other one can make the perturbed hybrid system almost surely stable with general decay rate. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation. [ABSTRACT FROM AUTHOR]

Summary: It is well known that a delay‐dependent or delay‐independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time‐varying or unknown delay, delay‐independent feedback laws are preferable over delay‐dependent feedback laws as the former provide robustness to the uncertainties in the delay. In the light of few results on the construction of delay‐independent output feedback laws for general linear systems with input delay, we present in this paper a delay‐independent observer–based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin‐type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open‐loop poles at the origin or in the open left‐half plane. Compared with that of the delay‐dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay. [ABSTRACT FROM AUTHOR]

Recently, a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC, the extremum seeker itself directly controls the systems through feedback rather than fine tuning a controller. The ESC results, and other related results, apply only to systems affine in control. However, in most physical systems, the control effort enters the system's dynamics through a nonlinear function, such as an input with deadzone and saturation. In this work, we use our previous results on ESC to develop constrained extremum seeking stabilizing controllers for systems of practical interest that are nonaffine in control. Considering that any odd function can be approximated arbitrarily well by an odd polynomial, we present analytic results for designing controllers for systems in which control enters the system dynamics through an odd polynomial. Furthermore, we study the robustness of the scheme to uncertainty in the odd polynomial degree as well as robustness to even-powered perturbations. [ABSTRACT FROM AUTHOR]

This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete-time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov- and coefficient-type sufficient criteria to guarantee the stabilization in the sense of [ABSTRACT FROM AUTHOR]

The paper investigates the problems of stability and stabilization of Markovian jump systems with time-varying delays and uncertain transition rates matrix. First, the stochastic scaled small-gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov-Krasovskii functional combined with Wirtinger-based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov-Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time-varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time-varying transition probabilities inside a polytope, we establish conditions under which the closed-loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the stabilization of a general linear heat-ODE system coupling at an intermediate point which is an extension from our previous work on stabilizing a coupled system of a heat PDE and a second-order ODE. A novel backstepping transformation is proposed which can overcome the difficulty of using the one proposed in our previous work to a more general system considered in the current paper. Existence of smooth kernels in both the forward and inverse transformations is proved. Also, we show that forward and inverse transformations are a mutually inverse pair governed by the kernels equations. Finally, the effectiveness of the controller design is demonstrated with some numerical examples for heat-ODE systems. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we apply the active disturbance rejection control approach to output-feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time-varying gain are used in ESO design separately. The mean square practical stability for the closed-loop system with constant gain ESO and the mean square asymptotic stability with time-varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Razumikhin-type approach is introduced to solve the state feedback stabilization problem for a class of stochastic high-order nonlinear systems with time-varying delay. Based on the general Razumikhin-type theorem on stochastic systems established in our paper and backstepping design method, a state feedback controller is constructed to ensure the origin of closed-loop system is globally asymptotically stable in probability. Our methodology enables us to completely remove the limitations on the derivative of delay, which is the common assumption of stochastic high-order nonlinear systems with time-varying delay. The efficiency of the state feedback controller is demonstrated by simulation examples. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic stability and stabilization problem for a general class of uncertain, continuous-time Markov jump linear systems (MJLSs). The system under consideration is a piecewise-homogenous Markovian structure subject to piecewise-constant time-varying transition rates (TRs). The time variation of the TRs is characterized by a high-level Markovian signal, which is independent from the low-level Markovian mechanism that governs the switching between the system dynamics. It is assumed that the structure is subject to mixed uncertainties in the form of additive norm-bounded terms. The uncertainties help to consider the effect of imperfections induced by modeling errors for the system dynamics and the TRs of Markovian signals of both levels. This new uncertain, two-level Markovian jump linear system is a more general model than the existing ones and is applicable to more practical situations. Besides, it is capable of being specialized to uncertain piecewise-homogeneous MJLS with arbitrarily varying TRs, as well as the uncertain time-homogeneous MJLS. The stability/stabilizability of this system is first examined by constructing a Lyapunov function which depends on both switching signals. Then, based on the analysis results, the corresponding robust controller gains are synthesized through solving a set of linear matrix inequalities (LMIs). Finally, simulation results for an industrial stirred tank reactor (CSTR) are used to demonstrate the applicability and potentials of the proposed theoretical method. Comparative simulations are also provided to show the superiority of the presented approach to the existing ones. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of stabilizing a time-varying nonlinear sampled-data system based on its approximate models. Given a time-varying nonlinear sampled-data system, we make use of the approximate models of the system at each sampling instant to build a time-varying approximate model with which an appropriate controller is designed. This paper provides some sufficient conditions under which a controller stabilizing the approximate models can also stabilize the exact sampled-data system under any sufficiently small sampling period. With this method, we do not need to compute the complicated exact discrete-time model of the concerned system and significantly simplify the controller design. The major contribution of this method lies in extending the available results regarding the time-invariant sampled-data systems to the time-varying case. Moreover, this method enables us to analyze the influence of the precision of approximate models on the system performance. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper focuses on stabilization on null controllable region of delta operator systems subject to actuator saturation via constructing suitable controllers. Under a saturated linear feedback law, a set of stable equilibrium points is obtained for the delta operator system with actuator saturation. A comprehensive controller is given to show global stabilization of the delta operator system. Thereby, semi-global stabilization of the delta operator system is also achieved. For higher-order systems with no more than two unstable exponentially poles, a new feedback law is constructed to achieve semi-global stabilization on the null controllable region. Finally, three examples are given to illustrate the effectiveness of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stabilization of discrete-time linear systems with a single input delay. By developing the methodology of pseudo-predictor feedback, which uses the (artificial) closed-loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed-loop system in terms of the stability of a class-difference equations. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open-loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the attitude stabilization problem of a rigid body, where neither the angular velocity nor the attitude is used in the feedback; only body-referenced vector measurements are needed. The proposed control scheme is based on an angular velocity observer-like system relying solely on vector measurements. The proposed controller ensures almost global asymptotic stability and provides some interesting performance properties through an appropriate tuning of the control gains. The performance and effectiveness of the proposed control scheme are illustrated via simulation results where the control gains are adjusted using a nonlinear optimization. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with robust stability and stabilization of linear discrete-time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic-like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed-loop model by means of a recent method based on robust control for discrete-time time-varying systems. Stability analysis and dynamic state-feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates almost sure exponential stability and feedback stabilization for switched time-delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non-convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean-square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. [ABSTRACT FROM AUTHOR]

This paper revisits the static output-feedback stabilization problem for positive systems. We first point out that for a class of positive systems whose output matrix has a particular row echelon form, this problem can be completely solved via linear programming. By duality, the result is also valid when the column echelon form of the input matrix has a particular structure. Along this line, by augmenting the output matrix as well as the feedback gain matrix, an iterative convex optimization algorithm is developed for the more general case. Finally, we show that the proposed method has advantages over existing works via several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Absolute stability with the spatially defined linear time-invariant (LTI) state-space modelings is scrutinized by means of what we call the sequential Lyapunov approach, which possesses independent significance in stabilization when gain-scheduling control laws are adopted. Then, this theoretical result is exploiting for stabilization of individual generators via SVC actions. More precisely, by remodeling the perturbed swing equations of synchronous generators in multimachine networks through spatially defined LTI state-space expressions subjected to uncertainties and power disturbance, which are viewed as sector nonlinearities, we introduce frequency responses for coping with nonlinear power swing dynamics of individual generators. By sequentially relating the frequency responses to the circle criterion (substantially, the KYP theorem or the positive real lemma) claimed for LTI systems subject to sector disturbances, output feedback control laws for static VAR compensators are worked out to stabilize individual generators. The frequency-domain approach is also useful in steady-state specification besides stabilization in individual generators. Examples show efficacy of the suggested stabilization and steady-state specification technique. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed-loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY We consider the stabilization of nonlinear ODE systems with actuator dynamics modeled by a wave PDE whose boundary is moving and is a function of time and of the ODE's state. Such a problem is inspired by applications in oil drilling where the position of the drill bit is a state variable in the ODE modeling the friction-dominated drill bit dynamics while at the same time being the position of the moving boundary of the wave PDE that models the distributed torsional dynamics of the drillstring. For moving boundaries that depend only on time, we extend the global result recently developed by Bekiaris-Liberis and Krstic for constant boundaries. For moving boundaries that also depend on the ODE's state, we develop a local result where the initial condition is restricted in such a way that it is ensured that the rate of movement of the boundary (both 'leftward' and 'rightward') is bounded by unity in closed-loop. For strict-feedforward systems under wave actuator dynamics with moving boundaries, the predictor-based feedback laws are obtained explicitly. The feedback design is illustrated through an example. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies local control of discrete-time periodic linear systems subject to input saturation by using The multi-step periodic invariant set approach. A multi-step periodic invariant set refers to a set from which all trajectories will enter a periodic invariant set after finite steps, remain there forever, and eventually converge to the origin as time approaches infinity. The problems of (robust) estimation of the domain of attraction, (robust) local stabilization (with bounded uncertainties), and disturbance rejection are considered. Compared with the conventional periodic invariant set approach, which has been used in the literature for local stability analysis and stabilization of discrete-time periodic linear systems subject to input saturation, this new invariant set approach is capable of significantly reducing the conservatism by introducing additional auxiliary variables in the set invariance conditions. Moreover, the new approach allows to design (robust) stabilizing periodic controller, in the presence of norm bounded uncertainties, whose period is the same as the open-loop system and is different from the existing periodic enhancement approach by which the period of the controller is multiple times of the period of the open-loop system. Several numerical examples are worked out to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the problem of stabilizing a linear system with input delay. Motivated by the first-order truncated predictor feedback (TPF) approach recently developed by the authors, a general higher-order TPF controller that contains higher-order terms of the nominal feedback gains is proposed. It is shown that this higher-order TPF can also globally and semi-globally stabilize the concerned time-delay systems in the absence and in the presence of input saturation, respectively. Safe implementation via numerical approximation of this higher-order TPF is also established. However, in spite of the fact that the higher-order TPF utilizes more information of the state, numerical examples have demonstrated that the first-order TPF outperforms the higher-order TPF, indicating that the intuition of higher-order approximation leading to better results is incorrect in this case.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY On the basis of a linear copositive Lyapunov function (LF) and a diagonal quadratic LF, respectively, two slow stabilizing switching laws are proposed for discrete time positive switched systems composed of [ABSTRACT FROM AUTHOR]

SUMMARY This paper investigates the problems of stability analysis and stabilization for stochastic time-delay systems. Firstly, this paper uses the martingale theory to investigate expectations of stochastic cross terms containing the Itô integral. On the basis of this, an improved delay-dependent stability criterion is derived for stochastic delay systems. In the derivation process, the mathematical development avoids bounding stochastic cross terms, and neither model transformation method nor free-weighting-matrix method is used. Thus, the method leads to a simple criterion and shows less conservatism. Secondly, on the basis of this stability result, this paper further proposes a state-feedback controller that exponentially stabilizes the stochastic delay system by a strict LMI. Therefore, unlike previous results, it is not necessary to transform the nonlinear matrix inequalities into LMIs by the cone complementarity linearization method or parameter-tuning method, which always yield a suboptimal solution. Finally, examples are provided to demonstrate the reduced conservatism of the proposed conditions.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we present a mechanism, called oscillation killer, intended to eliminate limit cycles that may occur as a consequence of unexpected external disturbances, interactions with the environment, changes in systems set-points, physical parameters, and so on. Examples range from controlled systems with friction to electrical networks with varying loads and impedances. The proposed mechanisms is shown to be particulary appropriate for nonlinear systems displaying a locally asymptotically equilibrium point surrounded by a locally asymptotically stable limit set outside this local domain. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]