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In this article, we propose a backstepping (BS)-based direct power control (DPC) strategy for the dual-cage rotor brushless doubly fed induction generator (DCR-BDFIG). The relationship between the power winding (PW) output power and the control winding (CW) voltage is derived according to the complete mathematical model of DCR-BDFIG. Based on that, a BS-based DPC controller, also known as a nonlinear controller, is designed with the global asymptotic stability analyzed for the grid-connected DCR-BDFIG. Compared with the dual-closed-loop control in the advanced vector control method, only single-closed-loop is required for the PW power in the proposed BS-based control scheme, and thus it has more simple structure and faster responses. The global stability of the proposed control scheme can be easily guaranteed with a Lyapunov function properly selected. In addition, in order to improve the performance of the proposed BS-based DPC strategy under unbalanced network, the resonant controller is introduced to suppress the oscillating components in the PW power, PW current, and CW current, whose harmonic order is twice of the grid frequency referring to the synchronous reference frame. Finally, the detailed experimental results demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques. [ABSTRACT FROM AUTHOR]

This article presents a novel Lyapunov-based model predictive control strategy for squirrel-cage induction motor fed by a voltage source inverter. The model predictive control method has received enormous attention thanks to its rapid response to load perturbations. However, the traditional model predictive control method may suffer from instability due to the poor choice of the objective function, weighting factors, or other design parameters. In particular, the selection of the objective function may not be sufficient to ensure global stability. Since the performance of the model predictive control method highly relies on the explicit model of the system, a simple penalization term in the objective function can lead to system instability. As a result, the transient and steady-state performances are negatively affected. The objective function is reformulated as the Lyapunov energy function to deal with this ambiguous situation in this article. The control input constraints are defined in the formulated optimal control problem, and the optimal solution is explored by assessing the Lyapunov stability criterion. The proposed method ensures asymptotic stability since the control action that satisfies the Lyapunov stability condition is selected. The experimental work proves the theoretical concepts. Moreover, the proposed method does not require the weighting factors to control the multiple control goals. The experimental results demonstrate that the proposed control strategy improves the steady-state performance. The machine torque and speed are well regulated, and the quality of the stator current is improved. [ABSTRACT FROM AUTHOR]

In this article, the problem of stability is investigated for a class of hybrid time-delay systems with double degrees. The systems consist of both discrete and continuous subsystems that have homogeneity and nonzero degrees. Conditions are derived to guarantee the preasymptotic stability of the systems. The relationships of solutions are established between the systems with different sizes using homogeneous properties. Then, equivalent conditions are presented for the analysis of preasymptotic stability. Furthermore, necessary and sufficient delay-independent conditions are developed to analyze the stability of the systems. Finally, two examples are provided to illustrate the effectiveness of the proposed new stability analysis methods. [ABSTRACT FROM AUTHOR]

For output-constrained switched systems, uniformly local stabilization problem via state feedback is addressed. A unified tool, a common tangent-type barrier Lyapunov function (Tan-BLF), is developed to deal with the stabilization problem of switched systems and to cope with constraints imposed on system output with or without. Then, combining adding a power integrator technique (APIT) and the developed common barrier Lyapunov function, state-feedback stabilizing laws are designed systematically to make the resultant closed-loop switched systems asymptotically stable while preventing the violation of output constraints. The efficiency of the proposed method is illustrated by numerical results. [ABSTRACT FROM AUTHOR]

This article investigates the fixed-time adaptive fuzzy containment control problem for nonlinear multiagent systems under the directed communication topologies. The controlled systems have the unknown internal dynamics and mismatched disturbances, and fuzzy logic systems are utilized to identify the unknown internal dynamics. The mismatched disturbances and approximate errors are reconstructed via a disturbance observer. Then, by introducing an adding power integral method, a fixed-time adaptive fuzzy containment DSC scheme is developed to deal with the problem of “computation complexity.” The presented containment control method can not only guarantee that the controlled system is semiglobal practical fixed-time stable, but also avoid the “singular problem” in fixed-time backstepping recursive control technology. Finally, an application of marine surface vehicle is provided to verify the effectiveness of the presented fixed-time fuzzy containment control method. [ABSTRACT FROM AUTHOR]

This article discusses the prescribed performance control problem for multiagent systems involving the state triggering and the controller output triggering simultaneously. To successfully apply the backstepping technique in the event-triggered control design, the virtual control signal is constructed by the original system state. Compared with the existing results on the prescribed performance, a new barrier Lyapunov function is developed with considering the characteristics of multiagent systems, and a fuzzy adaptive event-triggered control protocol is proposed by the backstepping procedure. It guarantees that the consensus tracking error converges to a predefined region of the origin in a preset finite time. At the same time, all other closed-loop signals remain bounded without the Zeno behavior. Finally, a simulation example confirms the availability of the developed control scheme with a comparison. [ABSTRACT FROM AUTHOR]

In this brief, emphasis is placed on the global uniform asymptotic stability analysis of a switched system formulated by cyclic or periodic switching laws. First, several concepts and properties of cyclic or periodically switched systems are defined. Next, by using the cycle dwell time or cyclic period time switching method, new stability criteria for cyclic or periodically switched systems with all Hurwitz stable sub-systems are obtained in the context of general solutions. Moreover, new stability conditions for cyclic or periodically switched systems with partially unstable sub-modes are derived in the framework of general solutions. Finally, two examples are provided to demonstrate the feasibility of the developed criteria. [ABSTRACT FROM AUTHOR]

This brief addresses the problem of global asymptotic stability for impulsive switched nonlinear systems (ISNSs) with double state-dependent delays (DSDDs), where the state-dependent delays exist in both subsystem functions and impulsive functions. The innovations of our results are that: 1) Due to the ubiquitous asynchronous phenomenon between the switches and impulses in many practical systems, we investigate the asynchronous phenomenon for ISNSs with DSDDs. 2) Meanwhile, the stabilizing and destabilizing effects of state-dependent delays impulses are fully considered. 3) By utilizing multiple Lyapunov functions, the switching strategy and the impulsive strategy, based on the asynchronous phenomenon, some stability criteria on global asymptotic stability are presented for ISNSs with DSDDs. As a result, the existing results are improved and can be regarded as a special case of the stability criteria in this brief. A simulation example is provided to verify the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

This article presents the input-to-state stability (ISS) and decentralized sliding-mode control of polynomial fuzzy interconnected systems by using the small-gain theorem. The contribution of this article is threefold. First, based on the boundedness of the solution of fuzzy interconnected subsystems, the sufficient conditions for the boundedness fuzzy interconnected system are provided. Second, the ISS small-gain theorem is extended to the polynomial fuzzy interconnected system for the number of membership functions being the same and different, and the trajectory-based ISS small-gain theorem is proposed. Third, the sliding surface based on state feedback is designed, and the stability of sliding-mode motion is analyzed for the fuzzy interconnected system. Finally, the effectiveness and superiority of the proposed method are illustrated by using a numerical example, a spring-connected double inverted pendulum system, and comparison with the existing results. [ABSTRACT FROM AUTHOR]

This brief is concerned with the issue of finite-time stabilization of discrete-time stochastic singularly perturbed models, in which the stochastic process is regulated by a Markov chain with partially unknown transition probabilities (TPs). The slow-state and fast-state variable are considered in the modeling, and the corresponding Markov switching model with a singularly perturbed parameter is obtained in a unified framework. Ill-conditioned problems caused by a small singular perturbation parameter are prevented by developing a finite-time stability criterion for the resultant system. Furthermore, feasible conditions are derived for the desired finite-time state feedback controller by using matrix inequalities that are independent of the singularly perturbed parameter. Finally, a gear-driven DC motor model is applied to illustrate the effectiveness of the described control strategy. [ABSTRACT FROM AUTHOR]

Abstract Tuberculosis (TB) is a contagious disease which can easily be disseminated in a society. A five state Susceptible, exposed, infected, recovered and resistant (SEIRs) epidemiological mathematical model of TB has been considered along with two non‐linear controllers: State Feedback (SFB) and Synergetic controllers have been designed for the control and prevention of the TB in a population. Using the proposed controllers, the infected individuals have been reduced/controlled via treatment, and susceptible individuals have been prevented from the disease via vaccination. A mathematical analysis has been carried out to prove the asymptotic stability of proposed controllers by invoking the Lyapunov control theory. Simulation results using MATLAB/Simulink manifest that the non‐linear controllers show fast convergence of the system states to their respective desired levels. Comparison shows that proposed SFB controller performs better than Synergetic controller in terms of convergence time, steady state error and oscillations.

This article presents the $L_1$ -gain polynomial fuzzy output-feedback controller design and the stability analysis using the sum-of-squares (SOS) approach for positive polynomial fuzzy-model-based (PPFMB) control systems. The polynomials, positivity, and optimal $L_1$ performance make some existing convex methods for general systems inapplicable. To overcome this problem, first, an augmented system of the PPFMB control system is constructed; then, by introducing some constraint conditions and mathematical techniques, nonconvex stability and positivity conditions are skillfully transformed into convex ones simultaneously. In addition, to control the systems flexibly and lower the implementation cost, the imperfect premise matching concept is taken into account for controller design. Besides, the high-degree-polynomial approximation method is adopted to conduct stability and positivity analysis by incorporating the information of membership functions and the boundary information of the state variables. On the basis of the Lyapunov stability theory, the relaxed stability and positivity conditions in terms of the SOS form are obtained. Finally, two simulation examples are presented to verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Existing studies on adaptive fault-tolerant control for uncertain nonlinear systems with actuator failures are restricted to a common result that only system stability is established. Such a result of not being asymptotically stable is a tradeoff paid for reducing the number of online learning parameters. In this article, we aim to obviate such restrictions and improve the bounded error control to asymptotic control. Toward this end, a resilient adaptive neural control scheme is newly proposed based on a new design of the Lyapunov function candidates, a projection-associated tuning functions method, and an alternative class of smooth functions. It is proved that the system stability is guaranteed for the case of an infinite number of failures and when the number of failures is finite, asymptotic tracking performance can be automatically recovered, and besides, an explicit bound for the tracking error in terms of $L_{2}$ norm is established. Illustrative examples demonstrate the methods developed. [ABSTRACT FROM AUTHOR]

This brief reports the prescribed-time stabilization (PST) problem for a class of uncertain planar nonlinear systems with output constraints. To handle the obstacle caused by the output constraints, a tan-type Barrier Lyapunov Function (BLF) that equates to the classical one for unconstrained systems is exploited. By suitably introducing the time-varying function into the virtual (actual) controllers rather than conventionally to scale the coordinate transformations, a switched, non-scaling design scheme for state feedback is developed to ensure that the origin of the resulting closed-loop system (CLS) is prescribed-time stable without disobeying the constraints. The novelty of the proposed control strategy is that it solves the computationally singular problem effectively and leads to a simpler controller in comparison with the traditional scaling design. Finally, the appealing performance of the proposed scheme is illustrated by simulation. [ABSTRACT FROM AUTHOR]

In this brief, a new Lyapunov-function-based event-triggered mechanism is proposed to investigate the state feedback control of nonlinear discrete-time cyber-physical systems. By summing the difference of Lyapunov-function between two adjacent events and utilizing it to construct the triggering law, the asymptotic stability of system can be ensured without demanding the difference of the Lyapunov function to be negative at any time. Thus, a larger inter-execution time under this scheme can be obtained than the conventional event-triggered mechanism. Meanwhile, the application of this scheme to linear systems is also presented. Finally, some simulations are implemented to show the advantages of the developed strategy. [ABSTRACT FROM AUTHOR]

This article is concerned with the problems of extended dissipativity analysis and filter design for interval type-2 (IT2) fuzzy systems. Based on the line integral Lyapunov function, a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established. A LMI-based equivalent condition to the obtained one in a nonlinear form is provided by combining congruence transformation with change of variables. This LMI condition obtained is more general than the one which is based on the common quadratic Lyapunov function. Meanwhile, in terms of parameterization, the extended dissipative filter is developed which guarantees the asymptotic stability and extended dissipativity for the filtering error system. Furthermore, our filter obtained by the parameterization method includes the one obtained by the equivalent transformation method as a special case. Two simulation examples are provided to show the merits and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article focuses on the conservativeness issue of the existing Lyapunov method for linear time-invariant (LTI) nabla fractional-order systems and proposes a converse Lyapunov theorem to overcome the conservative problem. It is shown that the LTI nabla fractional-order system is asymptotically stable if and only if there exist a positive-definite Lyapunov function whose first-order difference is negative definite. After developing a systematic scheme to construct such Lyapunov candidates, the Lyapunov indirect method is derived for the nonlinear system. Finally, the effectiveness and practicability of the proposed methods are substantiated with four examples. [ABSTRACT FROM AUTHOR]

Power system control and transient stability analysis play essential roles in secure system operation. Control of power systems typically involves highly nonlinear and complex dynamics. Most of the existing works address such problems with additional assumptions in system dynamics, leading to a requirement for a complete and general solution. This paper, therefore, proposes a novel control framework for various power system control and stability problems leveraging a learning-based approach. The proposed framework includes a two-module structure that iteratively and jointly learns the candidate Lyapunov function and control law via deep neural networks in a learning module. Meanwhile, it guides the learning procedure towards valid results satisfying Lyapunov conditions in a falsification module. The introduced termination criteria ensure provable system stability. This control framework is verified through several studies handling different types of power system control problems. The results show that the proposed framework is generalizable and can simplify the control design for complex power systems with the stability guarantee and enlarged region of attraction. [ABSTRACT FROM AUTHOR]

For uncertain systems with relative degree two, an output feedback based twisting algorithm is proposed. This algorithm ensures practical asymptotic convergence to the origin based on the information of output and its artificially delayed version. We prove the convergence of the proposed algorithm by a continuous, weighted homogeneous and strict Lyapunov function. [ABSTRACT FROM AUTHOR]

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi–Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the $\ell _{1}$ -stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under $\ell _{1}$ -induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]

This article considers local stability analysis and local stabilization of discrete-time nonlinear systems represented by Takagi–Sugeno fuzzy models. Conditions are established using Lyapunov functions and controller gains that depend also on past samples. Together with the stability and design conditions, an estimate of the region of attraction is also determined. The developed conditions are discussed and illustrated on several examples. [ABSTRACT FROM AUTHOR]

We present a reset control approach to achieve setpoint regulation of a motion system with a proportional-integral-derivative (PID)-based controller, subject to Coulomb friction and a velocity-weakening (Stribeck) contribution. While classical PID control results in persistent oscillations (hunting), the proposed reset mechanism induces asymptotic stability of the setpoint and significant overshoot reduction. Moreover, robustness to an unknown static friction level and an unknown Stribeck contribution is guaranteed. The closed-loop dynamics are formulated in a hybrid systems framework, using a novel hybrid description of the static friction element, and the asymptotic stability of the setpoint is proven accordingly. The working principle of the controller is demonstrated experimentally on a motion stage of an electron microscope, showing superior performance over classical PID control. [ABSTRACT FROM AUTHOR]

Diabetes mellitus type 1 occurs when β‐cells in the pancreas are destroyed by the immune system. As a result, the pancreas cannot produce adequate insulin, and the glucose enters the cells to produce energy. To elevate the glycaemic concentration, sufficient amount of insulin should be taken orally or injected into the human body. Artificial pancreas is a device that automatically regulates the level of body insulin by injecting the requisite amount of insulin into the human body. A finite‐time robust feedback controller based on the Extended Bergman Minimal Model is designed here. The controller is designed utilizing the backstepping approach and is robust against the unknown external disturbance and parametric uncertainties. The stability of the system is proved using the Lyapunov theorem. The controller is exponentially stable and hence provides the finite‐time convergence of the blood glucose concentration to its desired magnitude. The effectiveness of the proposed control method is shown through simulation in MATLAB/Simulink environment via comparisons with previous studies. [ABSTRACT FROM AUTHOR]

This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example. [ABSTRACT FROM AUTHOR]

Lyapunov method is a powerful tool for studying the stability of dynamic systems while existing work mainly focuses on the asymptotic stability and rarely concerns the boundedness. Under this background, this brief aims to discuss the boundedness of nonlinear nabla fractional order systems. By employing the nabla Laplace transform, two stability criteria in form of Lyapunov theorem are derived. Finally, two numerical examples are provided to evaluate the effectiveness and practicability of the theoretical results. [ABSTRACT FROM AUTHOR]

The Transmission Control Protocol (TCP) utilizes a congestion avoidance and control mechanism as a preventive measure against congestive collapse and as an adaptive measure in the presence of changing network conditions. The set of available congestion control algorithms is diverse, and while many have been studied from empirical and simulation perspectives, there is a notable lack of analytical work for some variants. To gain more insight into the dynamics of these algorithms, we: (1) propose a general modeling scheme consisting of a set of functional differential equations of retarded type (RFDEs) and of the congestion window as a function of time; (2) apply this scheme to TCP Reno and demonstrate its equivalence to a previous, well known model for TCP Reno; (3) show applications of the new framework to the widely-deployed congestion control algorithm TCP CUBIC, for which analytical models are few and limited; as well as to H-TCP, another high-speed congestion control algorithm; and (4) validate the model using simulations. Our modeling framework yields a fluid model for window- or rate-based congestion control variants. From a theoretical analysis of this model with TCP CUBIC, we discover that CUBIC is locally uniformly asymptotically stable – a property of the algorithm previously unknown. Through further analysis, we derive a sufficient condition for H-TCP’s stability, but observe via a numerical analysis and simulations that H-TCP rarely converges to an equilibrium and is usually not asymptotically stable in practical high-speed settings. [ABSTRACT FROM AUTHOR]

The main aim of this article is to design the observer-based event-triggered (ET) fuzzy integral sliding mode control (ETFISMC) for the generalized Takagi–Sugeno (T–S) fuzzy system which is formulated from a nonlinear system through blending the membership grades altogether. Distinct to the existing controller schemes, the proposed fuzzy integral sliding mode control (FISMC) scheme contains the ET condition which needs to be satisfied for the activation of the controller. Besides that, the network-induced communication constraints are considered into the derivation of sufficient conditions, and then the corresponding stabilization issue is attenuated in the sense of $H_{\infty }$ control performance. In addition, the appropriate Lyapunov–Krasovskii functional (LKF) candidate is constructed and evaluated through convex matrix inequality approach that ensures the stable $H_{\infty }$ performance of the closed-loop system in terms of solvable linear matrix inequalities (LMIs). Further, instead of considering the general problem for the validation of the proposed result, the stabilization problem of nonlinear chaotic permanent magnet synchronous generator (PMSG) model is taken into account for the validation of the proposed sufficient conditions. The purpose of considering the PMSG model is because of its significance in the wind energy conversion systems. [ABSTRACT FROM AUTHOR]