Stability of switched singular time delay systems with switching induced state jumps. Issue 19 (11th February 2021)

• Record Type: Journal Article
• Authors: Lin, Jinxing; Wu, Xiang; Ding, Jie; Lou, Zhi‐E
• Is Part Of: IET control theory & applications. Volume 14:Issue 19(2020)
• Page Start: 3351
• Page End: 3361
• Publication Date: 2021-02-11
• Subjects: time‐varying systems -- asymptotic stability -- stability -- linear systems -- uncertain systems -- Lyapunov methods -- continuous time systems -- linear matrix inequalities -- delays -- delay systems; arbitrary two adjacent switches -- time length -- switching instants -- time‐varying interval -- considered state delay varies -- switched singular state‐delayed systems -- exponential stability -- state jump -- switched singular time delay systems -- fast time‐varying function -- dwell time -- stability condition -- dwell‐time‐dependent function -- dwell‐time‐dependent generalised Lyapunov function -- dwell‐time switching constraint; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2019.1338
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : This study addresses the problem of exponential stability for switched singular state‐delayed systems with switching induced state jumps, which has not been studied up to now. The considered state delay varies in a time‐varying interval. On the basis of equivalent dynamics decomposition, a model of state jump at switching instants is firstly established under an assumption that the time length between arbitrary two adjacent switches is larger than the upper bound of the state delay. Then, a sufficient condition on exponential stability of the system under the reranged dwell‐time switching constraint is presented. The key idea is the design of a dwell‐time‐dependent generalised Lyapunov function as well as a dwell‐time‐dependent function with respect to algebraic variables and application of the Razumikhin approach. The obtained stability condition exploits the lower bound and the upper bound of the dwell time. In addition, it is independent of the size of the state delay and allows the delay to be a fast time‐varying function. Finally, two numerical examples are given to show the efficacy of the derived result.