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This work focuses on the robust leader-follower synchronization navigation for the under-actuated vessels with only independent the surge control force and the yaw moment. The ocean disturbances and thruster saturation are simultaneously addressed. A virtual vessel placed at the relative distance with the moving main vessel alleviates the requirements on main vessel's velocity measurements. The disturbance estimation performance is achieved by utilizing the disturbance observer. The additional controls produce the filtered non-achievable command control signals due to the thrust saturation effects. The filtered signals correct feedback errors for avoiding disturbance estimation and rejection compromise. The dynamic surface control technique is employed to derive the under-actuated synchronization control laws. By employing first-order filters, the differential terms are replaced by the algebraic operations such that the control is convenient to implement. It is analyzed that the supply vessel control system is semi-globally stable and the synchronization navigation along with the main vessel is ensured with the small errors. Simulations in the different disturbance cases validate the synchronization scheme.

This paper explores the delay dependent stochastic stabilization of Markovian jump neutral systems (MJNS) which are modeled by fractional Brownian motion(fBm) via a quantized controller. A function Round quantizer is introduced which solves the model uncertainties and the nonlinear part by a uniform operator. Then by structuring a Lyapunov-Krasovskii functional colorblue(LKF) and the aid of linear matrix inequalities (LMIs) method, a stochastic stability criterion is achieved. Last, different parameters are selected to simulate the effectiveness of our findings.

In this article, a decentralized adaptive finite-time tracking control scheme is proposed for a class of nonstrict feedback large-scale nonlinear interconnected systems with disturbances. First, a practical almost fast finite-time stability framework is established for a general nonlinear system, which is then applied to the design of the large-scale system under consideration. By fusing command filter technique and adaptive neural control and introducing two smooth functions, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented, while the obstacles caused by unknown interconnections are overcome. Moreover, according to the framework of practical almost fast finite-time stability, it is shown that all the closed-loop signals of the large-scale system are almost fast finite-time bounded, and the tracking errors can converge to arbitrarily small residual sets predefined in an almost fast finite time. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed finite-time decentralized control scheme.

This paper is devoted to the interval type-2 (IT2) fuzzy exponential stability for nonlinear networked sampled-data control systems with random communication links. By using the input delay approach, the designed networked IT2 fuzzy sampled-data controller can be applied in the continuous-time controlled plant, and the continuous-time Lyapunov–Krasovskii functional (LKF) is constructed. Based on the LKF theory, the stability analysis is conducted in the sense of mathematical expectation, and the sufficient conditions are determined in terms of the linear matrix inequalities. Then, the IT2 fuzzy networked controller is developed such that the networked closed-loop control system is exponentially stable. Finally, the simulation results are used to demonstrate the efficiency of the proposed design. The merits of the proposed algorithm are also shown by some comparative results.

This brief is devoted to exploring the global Mittag-Leffler (ML) synchronization problem of fractional-order memristor neural networks (FOMNNs) with leakage delay via a hybrid adaptive controller. By applying Fillipov's theory and the Lyapunov functional method, the novel algebraic sufficient condition for the global ML synchronization of FOMNNs is derived. Finally, a simulation example is presented to show the practicability of our findings.

This paper deals with the interval type-2 (IT2) fuzzy tracking control problem for nonlinear networked control systems with unreliable communication links. The plant is described by an IT2 fuzzy system, and the IT2 fuzzy sampled-data tracking controller is designed under the unreliable communication mechanism. By utilizing the Lyapunov theory, the stability demonstration is carried out under the mathematical expectation. The characteristics of membership functions are applied to enhance the stability of the IT2 fuzzy system. With the more sampling information used in the stability analysis, the less conservative sufficient condition is provided based on which a networked tracking controller is designed to ensure the anticipant tracking performance. Finally, the efficiency and the merits of this paper are shown by two simulation examples.

This paper deals with the issue of reliable sliding mode control for descriptor systems with semi-Markov parameters using the Takagi–Sugeno fuzzy model, in which an average dwell time approach is utilized to tackle generic uncertain transition rates (TRs). From the analysis of the inner mechanism of switching singular system, a continuous sliding surface function is proposed. Different from continuity with probability one for stochastic systems, the absolute continuity of system solution is a key point in this paper being ensured for application of the average dwell time approach. Then, the mean-square exponential stability of the obtained sliding mode is analyzed based on two types of uncertain TRs. Moreover, a sliding mode controller is constructed to ensure the reachability condition in finite time. Lastly, the method is verified numerically by a single-link robot arm model.

This paper is devoted to investigating the dynamic output feedback (DOF) control problem of Markovian jump neutral-type stochastic systems with a guaranteed cost function. Both of the state and measurement equations contain time delays. Mode-dependent DOF controllers are first designed such that the closed-loop system is asymptotically stable in mean-square and an adequate performance level of this system is guaranteed. Then, sufficient conditions for the solvability of this problem are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to reveal the effectiveness of our findings.

In this article, the issue of sliding mode control for nonlinear stochastic Markovian jump systems with uncertain time-varying delay is investigated. Considering the system state measurements and the state-dependent disturbances are not available for feedback purposes, an observer-based adaptive control strategy is proposed. Based on the decomposition of the input matrices, the state-space representation of the system is turned into a regular form with the aid of T–S fuzzy models first. Then, a fuzzy observer system is constructed, which could be transformed into two lower order subsystems. By choosing a common linear switching surface, on which it also obtains linear sliding mode dynamics in a simple form. Further, an adaptive controller is synthesized relying on the bounded system delay information to ensure the estimated states driven on the predefined sliding surface and remain the sliding motion. Also, the stochastic stability analysis of the sliding mode dynamics is undertaken with two types of transition rates, and an interesting result reveals that the stability for the dynamics with type of uncertain transition rates may cover the completely known type. Finally, a single-link robot arm model is provided to verify the validity of the proposed method.

When working at extremely high altitude, aerodynamic surfaces of air-breathing hypersonic vehicles (AHVs) may not provide sufficient control authority. To remedy this shortage, we consider AHVs equipped with the auxiliary reaction control system (RCS), which utilize a set of control jets to compensate for ineffective aerodynamic surfaces. A novel longitudinal compound control is proposed to generate commands of aerodynamic surfaces and RCS, adaptively. Constrained angle-of-attack, uncertain parameters, and flexible dynamics are also considered.

In this paper, a novel robust adaptive control scheme is developed for the trajectory tracking of surface vessels in the presence of dynamic uncertainties, unknown time-varying disturbances and input and output constraints. Firstly, the output constraint problem is transformed into the constraint problem of trajectory tracking error by coordinate transformations. Then, a nonlinear transformation is introduced to transform the tracking error into the transformed variable, with the aid of which the output constraint problem of surface vessel trajectory tracking is transformed into the boundedness problem of transformed variable, such that the various types of output constraint boundaries including constant, time-varying, symmetry and asymmetry ones can be handled in a unified framework. An auxiliary dynamic system (ADS) is applied to handle the input saturation effect. Incorporating the nonlinear transformation, the radial basis function neural networks and the ADS into dynamic surface control technique, a novel robust adaptive neural trajectory tracking control law is designed. It is theoretically proved that all signals in the closed-loop trajectory tracking control system of surface vessels are locally uniformly ultimately bounded and the actual positions and heading of surface vessels are guaranteed to lie in the constrained region. Simulation results on a scale model vessel illustrate the effectiveness of the proposed control scheme.

The problem of composite anti-disturbance control for semi-Markovian jump systems (S-MJSs) with time-varying delay via disturbance observer is analysed in this study. Unlike the existing methods, generally uncertain transition rates, time-varying delay, multiple disturbances, the H ∞ performance and disturbance-observer-based control (DOBC) are all considered in S-MJSs. The method which combines DOBC and H ∞ control is used to guarantee the system performance level of time-varying delay S-MJSs. Firstly, a sufficient condition of stochastic stability in the H ∞ performance level for the composite control system is given by using piecewise Lyapunov–Krasovskii functional. Secondly, the optimal value of disturbance suppression level for the system is solved by an optimisation algorithm. Thirdly, variation interval of time-delay has been divided into equal small intervals for reducing the conservatism of the method which addresses the mode-dependent time-delay problem. Furthermore, the composite controller and disturbance observer which satisfy the proposed stability condition are designed to address the composite anti-disturbance control problem of the closed-loop system. Finally, two practical systems are provided to testify the accuracy of research methods.

This article is devoted to the exponential stabilization problem of time-varying delay switched systems with nonlinear uncertainties via sliding mode technique. First of all, anon-fragile observer is established to deal with the case that the partial or total measurement of state variables is unavailable, from which a new sliding manifold is constructed. An exponential stability criteria of the dynamics in sliding phase is then devised in accordance with Lyapunov stability theory, linear matrix inequality and average dwell time method. Furthermore, the arrival condition of the designated sliding manifold is satisfied by utilizing the developed adaptive sliding mode controller. At last, the feasibility of the proposed control scheme is confirmed through two illustrative examples.

This study tends to solve the H ∞ finite-time boundedness (FTB) problems for discrete switched singular systems with time-varying delays via a non-fragile sliding mode approach. The remarkable feature of the provided method is that a new sliding surface function is constructed such that a full-order dynamic system is acquired. Thus, a non-fragile sliding mode controller can be proposed to guarantee the FTB of the dynamic system. Therein, by employing the multiple Lyapunov-like functions and dwell time (DT) method, sufficient conditions and the DT of switching signal are given to ensure the FTB of the sliding mode dynamics. These results are then applied to the H ∞ FTB issue, being expressed as a solvable optimisation problem. Furthermore, by employing a discrete reaching condition, the proposed sliding mode controller can guarantee the reachability of the quasi-sliding mode. The validity of the proposed theorems is verified through a numerical example.

In this study, an observer-based adaptive sliding mode control scheme is proposed for a class of uncertain switched systems. A state observer is utilised to estimate the unmeasured state variables, from which a novel sliding surface is provided. Based on linear matrix inequality technique, Lyapunov stability theory and the average dwell time approach, exponential stability of the overall closed-loop switched system is guaranteed by virtue of the proposed control scheme. An adaptive reaching motion control law is then developed to ensure the state trajectory can be driven onto the predesigned sliding surface in finite time. At last, the validity of the proposed method is demonstrated by simulation results.

The issue of observer-based adaptive sliding mode control of nonlinear Takagi–Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an ${H}_{\infty }$ performance disturbance attenuation level ${\gamma }$ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

This study concerns with the projective synchronisation problem of fractional variable-order master-slave systems via the fractional sliding mode control. Firstly, an applicative index law is designed for the considered fractional variable-order system based on the Grunwald-Letnikov definition. Secondly, two different fractional variable-order sliding surface functions are proposed to study this projective synchronisation problem. Meanwhile, sufficient conditions are obtained to ensure the projective synchronising error is asymptotically stable. Finally, numerical examples show the validity and feasibility of the proposed approach.

This paper is devoted to the investigation of the interval type-2 (IT2) fuzzy sampled-data stabilization problem for the controlled plant subject to nonlinearities and parameter uncertainties. Some free-weighting matrices, slack matrices, and the bound information in membership functions are used to improve the stability analysis. Based on the Lyapunov–Krasovskii functional (LKF) theory, a new relaxed sufficient condition with fewer linear matrix inequality (LMI) constraints is derived. According to this criterion, the IT2 fuzzy sampled-data controller is devised to ensure the closed-loop system is asymptotically stable. Finally, three practical examples are provided to demonstrate the effectiveness and efficiency of the proposed design. Some comparisons show that the proposed algorithm is more simple and practical.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

This paper focuses on the study of tracking control problem for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems with completely unknown control gains under input saturations. A hyperbolic tangent function is introduced to approximate the input saturation nonlinearity. Based on the above, a novel robust adaptive neural network (NN) tracking control scheme is proposed combining finite-time nonlinear tracking differentiator (FTNTD), Nussbaum-type function and adaptive NN with backstepping design tool. Within our scheme, a constructed novel nonlinear function featured by “small-error large-gain and large-error small-gain” is inset into virtual and actual control laws to achieve a balance between the feedback control gain and the system control performance and prevent the over-learning of parameter adaptive laws caused by the input saturation. By means of a newly constructed non-quadratic Lyapunov function, it is theoretically shown that all the signals in the closed-loop control system are semi-globally uniformly ultimately bounded. Finally, the effectiveness of our proposed scheme is verified by the simulations of two simulation examples.

We work on the investigation of the H ∞ performance for uncertain stochastic singular Markovian jump systems with both nonlinear external disturbance and general unknown transition rates (TRs) in this paper. There exist uncertainties in both parameters and TRs. Every transition rate could be totally unavailable or only its estimated value is available. With a generalized H ∞ disturbance attenuation level γ , some robust controllers are designed such that the delayed singular Markovian jump system is stochastically admissible. The novel controllers designed in this paper consist of an adaptive controller and a linear controller. Moreover, some sufficient linear matrices inequalities (LMIs) conditions are provided according to Lyapunov stability theory and It o ˆ ’s differential formula. Finally, an example is presented to demonstrate our main results.

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.

The problem of interval type-2 (IT2) fuzzy sampled-data stabilization is addressed for nonlinear continuous-time systems with time-varying delay and parameter uncertainties. The input-delay approach together with free-weighting and slack matrices is utilized to enforce the stability analysis, and a sufficient condition is formulated. Based on the condition, an IT2 fuzzy sampled-data controller is developed such that the closed-loop system is asymptotically stable. Illustrative examples are used to manifest the merits of this design.

This study is concerned with the problem of finite-time filter design for a class of Ito stochastic systems with Markovian switching and distributed time-varying delays. Firstly, a partially mode-dependent filter is designed to accommodate to unreliable network transmission. The attention is focused on deriving sufficient conditions for the filtering error system to ensure the finite-time boundedness and to satisfy a prescribed disturbance attenuation. Then based on stochastic functional theory, the existence of filter is presented by solving existing linear matrix inequalities optimisation problems. Furthermore, the result is extended to the case where the mode information is completely transmitted. Finally, a numerical example is provided to show the effectiveness of the proposed results.

The problem of sliding mode control design for nonlinear switching semi-Markovian jump delayed systems is investigated in this paper. By choosing a linear switching surface function, we first derive reduced-order sliding mode dynamics; Then, the property of sliding mode dynamics with generally uncertain transition rates is analyzed by checking a set of new conditions; Further, an adaptive sliding mode control law is constructed to ensure the finite-time reaching condition. Finally, a practical example is provided to disseminate the effectiveness of the proposed method numerically.

This paper addresses the issue of robust fuzzy sliding mode control for continuous-time nonlinear Takagi–Sugeno fuzzy systems with semi-Markovian switching. The focus is on designing a novel fuzzy integral sliding surface without assuming that the input matrices are the same with full column rank and then developing a fuzzy sliding-mode controller for stochastic stability purpose. Based on Lyapunov theory, a set of newly developed linear matrix inequality conditions are established for stochastic stability of the sliding-mode dynamics with generally uncertain transition rates, and then extended to where the input matrix is plant-rule-independent, as discussed in most existing literatures. Furthermore, finite-time reachability of the sliding surface is also guaranteed by the proposed fuzzy sliding-mode control laws. A practical example is provided to demonstrate the effectiveness of the established method numerically.

This paper is concerned with the problem of interval type-2 (IT2) fuzzy sampled-data $H_{\infty }$ control for nonlinear networked control systems with parameter uncertainties, data dropout, and transmission delay. The IT2 fuzzy system used to describe the networked control systems and the IT2 networked sampled-data controller implemented by a zero-order holder is connected in the closed-loop system. By means of the input delay approach, the resulting closed-loop system is converted into a continuous-time delayed system. Subsequently, the continuous-time Lyapunov–Krasovskii functional theory is used to carry out the stability analysis. Some slack matrices and the bound information in membership functions are introduced to obtain the relaxed sufficient conditions formed by the linear matrix inequalities, which guarantee the anticipant $H_{\infty }$ performance. Finally, the efficiency and merits of the proposed design method are verified by four practical systems.

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.

This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results.

In this paper, the issue of robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays is investigated via sliding mode control (SMC). A sliding mode strategy is presented combined with the observer technique, since the system states are unmeasured. The distinguishing feature of the provided strategy is that a novel sliding surface is constructed based upon the estimated states such that the resulting full-order closed-loop system is generated. Furthermore, by employing Lyapunov-Krasovskii functional, new sufficient criteria in terms of a solvable linear matrix inequality (LMI) is derived, insuring that the closed-loop system is admissible with an H∞-norm bound. With the solution of the LMI, a corresponding sliding mode controller is obtained for reaching motion and reducing the chattering. At last, the theoretical results are verified in numerical tests.

This paper treats the problems of stochastic stability, ℒ1-gain and control synthesis for positive semi-Markov jump systems (S-MJSs). The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing works have some conservation. To deal with these problems, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear co-positive Lyapunov function. Then, some sufficient conditions for ℒ1-gain constraint are also presented, upon which, a state feedback controller is designed by decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable with ℒ1-gain performance in the form of standard linear programming (LP). The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, numerical examples are given to demonstrate the validity of the main results.

This paper is concerned with disturbance-observer-based control for Markovian jump systems with time delay and actuator saturation. By virtue of the disturbance-observer-based control technique and an appropriate mode-dependent Lyapunov–Krasovskii functional, an anti-disturbance controller is designed to ensure that the resulting closed-loop systems are stochastically stable, as well as estimation of the domain of attraction. Furthermore, an iterative optimization method is proposed to acquire the maximum estimate of the domain of attraction by solving a set of linear matrix inequalities. Finally, a simulation illustrates the effectiveness of the proposed schemes.

The paper deals with the problem of finite-time stabilization for stochastic systems with time-varying delay by defining a new criterion for finite-time stability. Firstly, by use of more appropriate Lyapunov-Krasovskii functional (LKF), the difficulties of finite-time stability confronted in system analysis and synthesis can be overcome. Then, a state feedback controller is constructed to guarantee the closed-loop system finite-time stable. New conditions for finite-time stability analysis as well as controller synthesis are established in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the main results.

This paper deals with the problem of controller design for time-delay system with stochastic disturbance and actuator saturation. By use of more appropriate Lyapunov–Krasovskii functional (LKF) and a new criterion for the domain of attraction, less conservative conditions for stochastic stability are proposed. Then, the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome. These sufficient conditions are derived in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the given results.

The paper is devoted to the investigation of observer-based H ∞ sliding mode controller design for a class of nonlinear uncertain neutral Markovian switching systems (NUNMSSs) with general uncertain transition rates. In this case, each transition rate can be completely unknown or only its estimate value is known. Firstly, an H ∞ non-fragile observer subjected to the general uncertain transition rates of the NUNMSSs is constructed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are founded. Secondly, the state-estimation-based sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval. Thirdly, an asymptotically stochastic stability criterion is established by utilizing a new-type Lyapunov function to guarantee the error system and sliding mode dynamics to be asymptotically stochastic stable with a given disturbance attenuation level. Finally, an example is provided to illustrate the efficiency of the proposed method.

The paper deals with the problems of exponential stability and L 1 -gain analysis for positive time-delay Markovian jump systems (MJSs) with switching transition rates. Another set of useful regime-switching model is given, which extends fixed transition rates to time-varying transition rates. By resorting to the linear co-positive Lyapunov function and average dwell time, sufficient conditions for exponential stability are proposed in terms of standard linear programming. Based on the obtained results, L 1 -gain performance is analyzed. Finally, an example is proposed to illustrate the validity of the main results.

This paper studies the robust observer-based sliding mode H ∞ control issue for discrete-time stochastic Markovian jumping systems (MJSs) subject to packet losses (PLs). Here, a state variable observer of an initial system is designed to estimate the state and a series of Bernoulli random variables is utilized to model the PLs, whose occurrence probability is allowed to be imprecise. Then, a linear switching function is constructed based on the estimated state space. The aim of our paper is to design an observer-based sliding mode H ∞ control strategy such that, the stochastic stability conditions with prescribed H ∞ performance are established for augmented MJSs under the PLs with imprecise occurrence probability, which is composed of the sliding mode dynamics and the error system. The linear sliding surface can be determined by solving some linear matrix inequalities (LMIs). In addition, by proposing an improved reaching condition, the desired robust observer-based H ∞ controller is designed in discrete-time setting to drive the system state from any initial one onto the designated sliding surface. Finally, the usefulness of observer-based H ∞ control method is demonstrated via some numerical simulations.

This paper treats the problem of anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity. The anti-windup compensator is designed such that the resulting system with mode-dependent time-varying delays and saturating actuator is stochastically stable and the domain of attraction is maximized. Sufficient conditions for the corresponding problem are proposed in terms of linear matrix inequalities. Finally, an example about R L C serial circuit demonstrates the validity of the proposed results.

Summary In this paper, the exponential mean-square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov-Krasovskii functional method, sufficient conditions on the exponential mean-square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.

The paper deals with the problems of passivity and passification for stochastic systems with Markovian switching and generally uncertain transition rates. The considered systems are more general, which cover uncertain transition rates and partly known transition rates as two special cases. By employing the multiple Lyapunov function and some free-weighting matrices, a state feedback controller is constructed such that the resulted closed-loop system is stochastically passive. Some sufficient conditions for the solution to the problem are derived in the form of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the validity of the main results.

This paper is concerned with the problem of robust finite-time sliding mode control (SMC) for a class of continuous-time uncertain neutral systems with time-varying delays. Firstly, based on the constructed sliding mode observer, an integral sliding surface is put forward on the estimation space. Secondly, the synthesized SMC law guarantees the finite-time reachability of the predefined sliding surface. Thirdly, through finite-time stability analysis, sufficient conditions are established to guarantee the required performance of the system during both reaching phase and sliding motion phase. Finally, a practical example is provided to verify the effectiveness of the proposed method.

In this paper, we study the issue of finite-time stabilisation for stochastic Markovian jump systems with time-varying delay by considering a new criterion on finite-time stability. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying the finite-time stability of the plant as well as controller synthesis are established in standard linear matrix inequalities. The practical example about a single-link robot arm model demonstrates the validity of the main results.

This paper investigates the problem of robust passivity-based sliding mode control (SMC) for uncertain singular systems with semi-Markov switching and actuator failures. The attention is focused on designing a common sliding surface to weaken the jumping effect and developing a sliding mode controller to accommodate to actuator faults for passification of the singular semi-Markovian jump system. Based on linear matrix inequality technique, sufficient conditions are derived to ensure the closed-loop system to be stochastically admissible and robustly passive. Then the finite-time reachability of the sliding surface is guaranteed by the proposed SMC law. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained result.

This study is concerned with the problem of robust H ∞ sliding mode control (SMC) of It o ^ stochastic delayed Markovian jump systems subject to parameter uncertainties and non-linear perturbations. Firstly, for the sake of practicality, a common integral sliding surface functional without time-varying delay is proposed. Then, by using linear matrix inequalities technique, sufficient condition for the robust mean-square exponential stability of the resulting closed-loop system with a prescribed disturbance attenuation level γ is derived. Moreover, a novel sliding mode controller is designed such that system trajectories can be kept on the sliding surface almost surely since the initial time. Finally, an example is provided to illustrate the effectiveness of the obtained result.