<inline-formula> <tex-math notation="LaTeX">$\mathcal H_{\infty }$</tex-math> </inline-formula> Control for 2-D Markov Jump Systems in Roesser Model

Abstract

This paper considers the problem of asynchronous $\mathcal H_{\infty }$ control for two-dimensional (2-D) Markov jump systems. The underlying system is described based upon the Roesser model. Especially, the hidden Markov model is employed when dealing with the asynchronization between a controlled system and a controller, and the relation between them is constructed through a conditional probability matrix. Based on the Lyapunov function technique, the asymptotic mean square stability and $\mathcal H_{\infty }$ noise attenuation performance are investigated for the closed-loop 2-D system. Moreover, the controller gain can be obtained by solving a convex optimization problem. An example is presented to show the effectiveness and potential of the proposed new design technique.