Stochastic H2/H∞H2/H∞ control for discrete-time systems with state and disturbance dependent noise

This paper is to study the discrete-time stochastic H2/H∞H2/H∞ control with state and external disturbance dependent noise. A necessary and sufficient condition for the existence of H2/H∞H2/H∞ control is presented, which transforms the H2/H∞H2/H∞ controller design into solving four coupled matrix-valued equations. Moreover, a recursive algorithm for solving the four coupled matrix-valued equations is also given.