Resilient asynchronous H∞ control designed for discrete-time Markov jump systems: Static output feedback case

Abstract

This article is concerned with the problem of resilient asynchronous H∞ static output feedback control for discrete-time Markov jump linear systems. By Finsler’s Lemma, and with the help of two sets of slack variables, the product terms of system matrices and Lyapunov matrices are decoupled. Resilient asynchronous controller is designed to improve the robustness of the controller and overcome the drawback that the controller cannot get the information of the system’s mode. The controller that makes sure the closed-loop system is stochastically stable and with prescribed H∞ performance is designed. The bilinear matrix inequalities are given as the sufficient conditions for the controller design, which can be solved using linear matrix inequalities along with line search. This control strategy can be used in many practical application fields, such as robot control, aircraft, and traffic control.