Asynchronous Static Output Feedback Control of Discrete-Time Markov Jump Systems

Abstract

The paper investigates the problem of $l_{2}-l_{\infty}$ asynchronous static output feedback control for discrete-time Markov jump linear systems. The hidden Markov model is applied to describe the asynchronization between the original system and the designed controller. Via the system augmentation technique, the closed-loop system is represented as a descriptor system. Based on stochastic Lyapunov function technique, a sufficient condition is developed to ensure that the closed-loop system is stochastically admissible with a given $l_{2}-l_{\infty}$ performance. By Finsler's lemma and the convexification approach, controller parameters can be obtained by solving a set of linear matrix inequalities. Finally, the applicability and effectiveness of the proposed approach is demonstrated by an example.