$H_{\infty}$ Optimal Control of Jump Systems Over Multiple Lossy Communication Channels

Abstract: In this paper, we consider the $H_{\infty}$ optimal control problem for a Markovian jump linear system (MJLS) over a lossy communication network. It is assumed that the controller communicates with each actuator through a different communication channel. We solve the $H_{\infty}$ optimization problem for 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 analyzed 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.