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

Abstract

Summary 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.

Reachable set estimation and synthesis of discrete‐time switched systems

“…5 On the other hand, reachable set acts a crucial performance index for switched systems. [21][22][23][24] The estimation of reachable set is an interesting topic, whose aim is to find a closed set which contains all possible system states starting from the origin. 25 Actually, reachable set is not only a fundamental concept in control theory [26][27][28] but also a practical engineering problem.…”

“…The reachable set estimation for switched systems with time-delay was investigated. 23,24 Chen et al 29 addressed the reachable set estimation and gave three optimization strategies for discrete-time switching systems. And Xiang et al 30 proposed a set of bounding ellipsoids to estimate reachable set by M-step sequence.…”

“…On the other hand, reachable set acts a crucial performance index for switched systems 21‐24 . The estimation of reachable set is an interesting topic, whose aim is to find a closed set which contains all possible system states starting from the origin 25 .…”

“…Ellipsoidal approach is an effective method to estimate reachable set via Lyapunov function. The reachable set estimation for switched systems with time‐delay was investigated 23,24 . Chen et al 29 addressed the reachable set estimation and gave three optimization strategies for discrete‐time switching systems.…”

Algebraic criteria for reachable set estimation of delayed memristive neural networks

“…In the framework of bounding ellipsoid, the quadratic Lyapunov function has played a fundamental role in the reachable set estimation of other complicated systems. For example, linear systems with both discrete and distributed delays [26, 27], neural networks with time‐varying delay [28], singular systems [29, 30], switched systems [31, 32], periodic systems [33, 34], T–S fuzzy systems [35], Markovian jump systems [36], positive linear systems [37] and so on. Very recently, reachable set estimation problem for MNNs with time‐delay was first investigated in [38] by LMI technique.…”