Infinite Horizon H_2/H_∞ Optimal Control for Discrete-Time Infinite Markov Jump Systems with (x, u, v)-Dependent Noise

摘要

This paper is concerned with the infinite horizon H_2/H_∞ control problem for a broad class of discrete-time infinite Markov jump systems with (x, u, v)-dependent noise. We first derive a linear quadratic optimal control problem (LQ problem, for short) for the considered system. Next, a necessary and sufficient condition is presented for the existence of the mixed H_2/H_∞ control by four coupled matrix Riccati equations (CMREs), and a state feedback H_2/H_∞ controller is constructed through the solution of CMREs.