\(H_2/H_{\infty}\) control design of detectable periodic Markov jump systems (Q1665552)

Summary: An infinite horizon \(H_2/H_{\infty}\) control problem is addressed for discrete-time periodic Markov jump systems with \((x, u, v)\)-dependent noise. Above all, by use of the spectral criterion of detectability, an extended Lyapunov stability theorem is developed for the concerned dynamics. Further, based on a game theoretic approach, a state-feedback \(H_2 / H_{\infty}\) control design is proposed. It is shown that under the condition of detectability \(H_2 / H_{\infty}\) feedback gain can be constructed through the solution of a group of coupled periodic difference equations.