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

• Published in: IEEE transactions on automatic control Vol. 66; no. 9; pp. 4274 - 4281
• Main Authors: Tian, Yongxiao, Yan, Huaicheng, Zhang, Hao, Zhan, Xisheng, Peng, Yan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Control systems design; Discrete time systems; Feedback control; Incomplete semi-Markov kernel (SMK); Indexes; Kernel; Kernels; Liapunov functions; linear semi-Markov jump systems (SMJS); Linear transformations; Markov chains; Markov processes; Mathematical analysis; mean-square stability; Numerical stability; Output feedback; piecewise homogeneous embedded Markov chain (EMC); resilient; RLC circuits; Stability criteria; static output-feedback; Time dependence
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3034199

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.