Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching

Stability and [formula omitted]-gain analysis for switched delay systems: A delay-dependent method

Some sufficient conditions for exponential stability of linear neutral functional differential equations

The stability analysis and L2‐gain for a class of switched neutral systems with all unstable subsystems are investigated in this paper. By constructing the discretized multiple Lyapunov‐Krasovskii functional and resorting to the time‐driven switching signals, sufficient conditions for exponential stability and weighted L2‐gain are developed for a class of switched neutral systems, where all subsystems are unstable. It should be pointed out that all the Lyapunov‐Krasovskii functional energies are allowed to increase during the running intervals of the active subsystems. Furthermore, all the conditions are formulated in forms of a set of linear matrix inequalities which can be easily solved by using the recently developed interior point method. Finally, two numerical examples are provided to show the effectiveness of the proposed approach.

This paper investigates the problem of sliding mode control (SMC) for uncertain switched stochastic system with time-varying delay. The system under consideration is concerned with the stochastic dynamics and deterministic switching laws. An integral sliding surface is constructed and the stable sliding mode is derived. A sufficient condition for mean-square exponential stability of the sliding mode is developed under a class of switching laws based on the average dwell time method. Variable structure controllers are designed to guarantee the existence of the sliding mode from the initial time. An illustrative example is used to demonstrate the effectiveness of the proposed scheme.

This paper presents a scheduling strategy for a collection of discrete-time networked control systems (NCSs) subjected to communication constraints. Communication constraints under consideration include medium access constraint, network-induced delays and packet-dropouts. A feedback control system with the communication constraints is modelled as a switched delay system which switches on the open-loop and closed-loop models according to whether the feedback control loop gains access to the network or not. Delay-dependent sufficient conditions for exponential stability with L 2 gain performance are developed for the switched system. Based on the stability conditions, sufficient conditions are presented on the existence of scheduling policy that simultaneously stabilizes the collection of NCSs. Simulation on network-based control of unstable batch reactor systems is performed to demonstrated the effectiveness of the proposed scheduling strategy.

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results.

The paper investigates mean-square exponential stabilization for a class of nonlinear switched stochastic systems with interval time-varying delay under asynchronous switching. Specifically, the delay occurs not only in the state equation, but also in the switching signal from the controller, which brings the difficulty of controller design to achieve mean-square exponential stabilization. Based on the Lyapunov stability theory, a new piecewise multi-Lyapunov–Krasovskii functional dependent on the size of time delay is constructed. By utilizing the matrix inequality technique and the average dwell time approach, delay-dependent sufficient conditions are given to guarantee mean-square exponential stabilization for nonlinear switched stochastic systems under asynchronous switching. In accordance with the method, we also design state feedback controllers of the switched stochastic systems under asynchronous switching through special operations of matrices and Schur complement. Finally, a numerical example and a practical example of river pollution control are provided to show the effectiveness of the approach proposed in this paper.

Stability analysis of discrete-time switched linear systems with unstable subsystems

This paper investigates the cooperative stabilization problem for a class of linear switched systems under asynchronous switching. Based on a novel class of switching signals which prevail over the traditional average dwell time scheme, a sufficient condition of global asymptotic stability is proposed for the considered system. Unlike the existing results, the provided condition permits the Lyapunov-like function to increase not only in the period of mode-identifying process but also in normal-working period with matched controller. Compensating the increment by an increased decrement, the proposed approach can guarantee the decrease of the Lyapunov-like function from a whole perspective. Moreover, the solvability condition is established as well to obtain the gains for corresponding controllers. Finally, a simulation example is provided to verify the validity of the presented method.

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

Stability analysis of 2D Roesser systems via vector Lyapunov functions

This paper investigates the problem of tracking control for a class of switched non-linear systems with time-varying delay. Firstly, based on the average dwell time method, a new exponential stability criterion for a class of switched non-linear systems with time-varying delay is derived; it is shown that this new criterion can provide fewer conservative results than those in the existing references. Then, tracking control for the systems is investigated, and a kind of state feedback control law and switching signal are proposed to satisfy the H∞ model reference tracking performance. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

This paper focuses on the finite-time boundedness of switched nonlinear systems based on the Finsler’s lemma, auxiliary matrices, and average dwell time method. The analysis is provided for a switched system with Lipschitz nonlinearities and in the presence of external disturbances. Moreover, a switching controller is designed based on linear matrix inequalities (LMIs), to make the closed-loop system finite-time bounded. Presented theorems in this paper are more general and have less conservatism than the existing methods due to using the auxiliary matrices that make the Lyapunov matrix separate from the system matrix in the resulting LMIs. Moreover, in all theorems, the average dwell time of the switching system has been evaluated. Three examples are given to illustrate the effectiveness of the proposed method and to show that it is less conservative compared with existing methods.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

This paper is dedicated to proposing improved input‐to‐state stability (ISS) criteria for a class of continuous‐time time‐varying switched singular systems (CTSSS) under slow/fast/slow‐fast switching signals. Specifically, for a CTSSS with time‐varying singular matrices, the authors start with an improved sufficient condition for verifying its ISS under slow switching signals based on the average dwell time method and a relaxed multiple Lyapunov function. Then, considering several or all subsystems may destroy the overall ISS, relaxed sufficient conditions are presented to ensure the ISS of the CTSSS under fast switching signals and slow‐fast switching signals, respectively. Note that the improvement of the proposed ISS criteria is embodied in the derivative of the required multiple Lyapunov functions along with the state trajectories of CTSSS can be positive or negative. Finally, three numerical examples are provided to illustrate the feasibility of the obtained results.