Stochastic H2 optimal control of discrete-time Markov jump systems with periodic coefficients

In this paper, the H₂ optimal state-feedback control problem is investigated for discrete-time Markov jump systems subject to periodic coefficients and multiplicative noise. First of all, an exhaustive analysis is pursued to set up an H₂ performance criterion (H₂ norm), which can be characterized by the periodic solutions of two generalized Lyapunov equations. Based on the obtained H₂ norm, the H₂ optimal state-feedback controller is designed in terms of the stabilizing solution of a discrete-time generalized Riccati equation with periodic coefficients. Moreover, this stabilizing solution can be computed efficiently by the available iterative algorithm.