H2/H∞Control Design of Detectable Periodic Markov Jump Systems

An infinite horizonH2/H∞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-feedbackH2/H∞control design is proposed. It is shown that under the condition of detectabilityH2/H∞feedback gain can be constructed through the solution of a group of coupled periodic difference equations.