Resilient Static Output Feedback Control of Linear Semi-Markov Jump Systems With Incomplete Semi-Markov Kernel

• 成果类型: Article
• 署名作者: Tian, Yongxiao; Yan, Huaicheng; Zhang, Hao; Zhan, Xisheng; Peng, Yan
• 署名单位: East China University of Science & Technology; East China University of Science & Technology; Hubei Normal University; Tongji University; Shanghai University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3034199
• 发表日期: 2021
• 页码: 4274-4281
• 关键词: Markov processes; kernel; indexes; Numerical stability; Stability criteria; Incomplete semi-Markov kernel (SMK); linear semi-Markov jump systems (SMJS); mean-square stability; piecewise homogeneous embedded Markov chain (EMC); resilient; static output-feedback

摘要

This article is concerned with the problem of the static output-feedback control for a class of discrete-time linear semi-Markov jump systems (SMJSs). Through a mode-dependent resilient control scheme and an invertible linear transformation, a resulting equivalent closed-loop system can be obtained. The embedded Markov chain (EMC) is piecewise homogeneous, which leads to incomplete semi-Markov kernel is variable in the finite interval. A novel class of multivariate dependent Lyapunov function is constructed, which is mode-dependent, elapsed-time-dependent, and variation-dependent. Numerically testable stabilization criteria are established for discrete-time linear SMJSs via abovementioned Lyapunov function. Under bound sojourn time, a desired stabilizing controller is designed such that the closed-loop system is mean-square stable. Finally, the theoretical results are applied to a practical RLC circuit system to show the effectiveness and applicability of the proposed control strategy.