Almost Sure Stabilization of Continuous-Time Jump Linear Systems via a Stochastic Scheduled Controller

• Published in: IEEE transactions on cybernetics Vol. 52; no. 5; pp. 2712 - 2724
• Main Authors: Wang, Guoliang, Sun, Yuanyuan
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Almost sure stability; Asymptotic stability; Control systems; Controllers; Dwell time; linear matrix inequalities (LMIs); Linear systems; Processor scheduling; Scheduling; Stabilization; stochastic jump systems; Stochastic processes; stochastic scheduling; Subsystems; Symmetric matrices; Transfer matrices
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.3021424

This article addresses the almost surely exponential (ASE) stabilization problem of continuous-time jump systems realized by a stochastic scheduled controller. In this study, a stochastic scheduled controller based on the anytime algorithm is proposed. It is able to cope with the situation where no controller is added to subsystems during some time slices. Sufficient conditions for the existence of such a controller are established by applying novel techniques to its stochastic transfer matrix, and they are all presented with solvable forms. Particularly, both dwell times of the jump signal and distribution properties of stochastic scheduling are considered and proved to have played positive roles in obtaining better performance and applications. Two special situations about no jump systems with constant and varied dwell times are further studied, respectively. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.