On singular hybrid switched and impulsive systems

Abstract

Summary In this work, the problem of stability analysis for a class of singular hybrid switched and impulsive system (HSIS) is addressed. Corresponding to each subsystem, a hybrid switched and impulsive controller is designed and then the exponential stability property of the proposed singular HSIS is discussed for linear and nonlinear cases. Because switched systems without impulses are a special case of HSISs, the results are also given to switched system with synchronous and asynchronous controllers. The obtained results apply to control singular systems, and the introduced theorems allow knowing how the control must be designed. Two numerical examples are given to show the effectiveness of the proposed approaches. At first, by using MATLAB® software, the proposed method is applied to a class of physiological processes of endocrine disruptor diethylstilbestrol models to illustrate the effectiveness of the results obtained here for the linear case. Thereafter, another numerical example is provided to support the presented theoretical results for the nonlinear case.

Synchronization of singular switched complex networks via impulsive control with all nonsynchronized subnetworks

“…Remark The stability of singular switched impulsive systems was discussed in the works of Zamani et al and Shi et al with the assumption that at least one subsystem must be stable. Intuitively, it should be more challenging when all the subsystems are unstable.…”

“…In the following, the impulsive controller is designed. According to the analysis in the works of Zamani et al and Shi et al, the two equations in should be satisfied at switching point. For ensuring that the last ( N −1)( n − r p ) rows of the right of the second equation in are zero, let and have the following form: where K p 1 , K p 2 are matrices that need to be determined by the later conclusions.…”

“…In the following, the impulsive controller is designed. According to the analysis in the works of Zamani et al 39 and Shi et al, 40 the two equations in (7) should be satisfied at switching point. For ensuring that the last (N − 1)(n − r p ) rows of the right of the second equation in (7) are zero, letΥ p1 andΥ p2 have the following form:…”

“…Assumption is satisfied with φ 1 = φ 2 =1, and all error subsystems in are not stable because , . Therefore, the methods in other works cannot be applied to achieve the synchronization problem of the aforementioned studied switched system that each subnetwork is not synchronous. However, Theorem can be used to solve this problem, as shown below.…”

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

“…There are some results on reachable set estimation reported on continuous‐time time‐delay linear systems under bounded peak disturbance in the literature. () However, to the best of the authors' knowledge, there are still no results on reachable set estimation for discrete‐time time‐delay switched system, which motivates the current study.…”