Discrete mathematics

Physics

Nonlinear system

Markov model

Mathematics

Variable-order Markov model

Kernel (algebra)

Markov chain

Statistics

Markov kernel

Mathematical optimization

Mathematical analysis

Artificial intelligence

Markov process

Control (management)

Computer science

Quantum mechanics

Applied mathematics

Control theory (sociology)

Discrete time and continuous time

Lyapunov function

Linear system

IEEE Transactions on Automatic Control

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.

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