H∞ Optimal control of jump systems over multiple lossy communication channels

Abstract

Abstract In this paper, the $H_{\infty }$ optimal control problem for a Markovian jump linear system (MJLS) over multiple lossy communication channels is considered. It is assumed that the controller communicates with each actuator through a different communication channel. We solve the $H_{\infty }$ optimization problem for the system with a Transmission Control Protocol (TCP) using the theory of dynamic games and obtain a state feedback controller. The infinite horizon $H_{\infty }$ optimization problem is analysed as a limiting case of the finite horizon optimization problem. Then, we obtain the corresponding state feedback controller and show that it stabilizes the closed-loop system in the face of random packet dropouts. A novel and relaxed condition for stability of the closed-loop system with the saddle-point policy is also presented. Further, we show that a weaker notion of observability is sufficient to establish our results.