Synchronization of Switched Neural Networks with Time‐varying Delays via Sampled‐data Control

This paper investigates sampled‐data synchronization control of switched neural networks with time‐varying delays under average dwell time. Based on the delay system method, the sampled‐data synchronization system is proposed with time‐varying delays and input delays in the unified framework for switched neural networks. By constructing a suitable Lyapunov‐Krasovskii functional and free‐weighting matrix, the relationship between the average dwell time and the maximum sampling interval is revealed to form delay‐dependent exponentially synchronization criteria. The desired mode‐dependent controller under the maximum sampling interval and decay rate is designed. Finally, two numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed techniques.     

Reachable set estimation for discrete‐time switched system with application to time‐delay system

This paper addresses the problem of reachable set estimation and synthesis for a class of discrete‐time switched linear systems with time delay and bounded peak disturbance. Combined with the feature of mode‐dependent average dwell time switching, a new algorithm is developed to estimate the reachable set of switched system, which is both quasi‐time‐dependent and mode‐dependent. Then, the proposed method is applied to time‐delay system and a sufficient condition is presented to guarantee the asymptotic stability and estimate the bounding ellipsoid. Furthermore, the quasi‐time‐dependent controller is designed to stabilize the system and restrict the closed‐loop system states to an ellipsoidal bound. Examples are presented to illustrate the effectiveness and advantages of the obtained theorems.     

Finite‐Time Stabilization of a Class of Cascade Nonlinear Switched Systems

This paper investigates the finite‐time stabilization problem for a class of cascade nonlinear switched systems. Using the average dwell time and multiple Lyapunov function technologies, some sufficient conditions to guarantee that the corresponding closed‐loop system is finite‐time stabilized are derived for the switched systems. Via multiple Lyapunov functions, the state feedback controller is designed to finite‐time stabilize a cascade nonlinear switched system, and the conditions are formulated in terms of linear matrix inequalities. An example is given to illustrate the efficiency of the proposed methods.     

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

A stability criterion for asynchronously switched linear systems via sampled‐data control

This paper considers an asynchronous problem for sampled‐data control of switched linear systems, which are described as switched linear systems with an input delay. To handle the problem, this paper proposes a stability criterion for the systems by constructing a novel Lyapunov‐Krasovskii functional dependent not on system modes but on controller modes. The functional continuously remains when the system modes are switched but discontinuously changes whenever the controller mode moves to the current system mode at the sampling instants. Furthermore, the functional is allowed to increase or decrease up to a certain level when the functional discontinuously changes and to increase up to a certain level when the system modes and the controller modes are asynchronous. Based on the functional, this paper derives an average dwell time associated with the interval of samplings and the incremental level of the functional for guaranteeing the stability of the systems. A numerical example illustrates the validation of the proposed method.     

Feedback passification of switched stochastic time‐delay systems with multiple disturbances via DOBC

This paper is concerned with the problem of feedback passification for switched stochastic time‐delay systems with multiple disturbances subject to mode‐dependent average dwell‐time switching. The multiple disturbances are composed of two parts: one is given through an exogenous system and the other is described in the form of norm‐bounded vector. A disturbance observer is constructed to estimate an exogenous disturbance. Then, a state feedback controller that includes the estimation value is designed to guarantee the passivity of the closed‐loop system. The observer and controller gains are developed via linear matrix inequalities. The effectiveness of the proposed method is verified through a numerical example and an application example to PWM‐driven boost converter.     

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

The dissipativity of discrete‐time switched memristive neural networks with actuator saturation is considered in this paper. By constructing a quasi‐time‐dependent Lyapunov function, sufficient conditions are obtained to guarantee the exponential stability and exponential dissipativity for the closed‐loop system with mode‐dependent average dwell time switching. Furthermore, the exponential H_∞ performance of discrete‐time switched memristive neural networks is also analyzed, while the quasi‐time‐dependent controller and observer gains of the desired exponential dissipative and H_∞ performance can be calculated from linear matrix inequalities. Finally, the effectiveness of theoretical results is illustrated through the numerical examples.     

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.     

Funnel‐like prescribed tracking control for uncertain nonlinear stochastic switched systems

This paper deals with the funnel‐like prescribed tracking control problem for a class of uncertain nonlinear stochastic switched systems. An improved performance technique is developed to restrain the fluctuation at the moment of switches and a new algorithm is proposed to address the funnel‐like prescribed tracking problem. First, a dynamic gain‐based switched K‐filter is constructed to estimate the unmeasured state information of the switched system. Subsequently, the performance technique is applied to prescribe output tracking error and restrain fluctuations of the system. Thereafter, the dynamic output feedback switched controller is designed by the use of the backstepping method. Moreover, based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed‐loop system are bounded in probability if the switching signal satisfies the average dwell time. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed theoretical results.     

Weighted‐average ℓ1 filtering for switched positive systems

In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ? ₁ disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ? ₁ disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ Control for a Class of Continuous‐time Switched Systems with State Constraints

This paper investigates the H_∞ control problem for a class of continuous‐time switched systems subject to state constraints with an improved average dwell time. The state constraints are converted into state saturations by limiting the state in a unit hypercube. By employing this proposed improved average dwell time method, which takes into account different decay rates of a Lyapunov function related to an active subsystem according to whether the saturations occur or not, the resulting minimum of admissible average dwell time is smaller than the one of the standard average dwell time, which only considers the same decay rate regardless of whether the saturations occur or not. In addition, switched state feedback controllers are designed such that the closed‐loop switched system, subject to state constraints, is asymptotically stable and achieves a weighted L₂‐gain. Sufficient conditions for H_∞ control of the switched system with state constraints are derived before an application to a Pulse‐Width‐Modulation (PWM)‐driven boost converter is given to illustrate the applicability and the effectiveness of the proposed method.     

L1‐Gain Analysis and Control for Switched Positive Systems with Dwell Time Constraint

This paper studies the problems of L₁‐gain analysis and control for switched positive systems with dwell time constraint. The state‐dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching. By constructing multiple linear co‐positive Lyapunov functions, sufficient conditions of stability and L₁‐gain property are derived under the proposed switching strategy. Then, an effective state feedback controller is designed to ensure the positivity and L₁‐gain property of the closed‐loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

A New Approach For Stability Analysis Of Time‐Dependent Switched Continuous‐Time Linear Systems

In this paper, a new approach for stability analysis of time‐dependent switched linear systems is proposed. System equivalence is the main idea in this new approach, which derives a switched discrete linear parameter‐varying system from the switched continuous‐time linear switched system with interval dwell time, and the stability properties of the two corresponding systems are proved to be equivalent. Then, by applying a quadratic Lyapunov function approach for the equivalent switched discrete system, the stability of the switched continuous‐time linear system can be established without checking any average dwell time condition. Finally the computation complexity is analyzed, and mode incidence matrix is introduced to reduce the computation cost.     

Delay‐Dependent Exponential Stability for Discrete‐Time Singular Switched Systems with Time‐Varying Delay

In this paper, the exponential stability problem is investigated for a class of discrete‐time singular switched systems with time‐varying delay. By using a new Lyapunov functional and average dwell time scheme, a delay‐dependent sufficient condition is established in terms of linear matrix inequalities for the considered system to be regular, causal, and exponentially stable. Different from the existing results, in the considered systems the corresponding singular matrices do not need to have the same rank. A numerical example is given to demonstrate the effectiveness of the proposed result.     

Delay‐dependent exponential H ∞ filtering for discrete‐time switched delay systems

In this paper, the problem of delay‐dependent exponential H _∞ filtering for discrete‐time switched delay systems is investigated under average dwell time switching signals. Time delay under consideration is interval time‐varying in the states. By introducing a proper factor to construct a novel Lyapunov‐Krasovskii function and using average dwell time approach, sufficient conditions for the solvability of this problem, dependent on the upper and lower bounds of time‐varying delay, are obtained in terms of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.