H 2 H ∞ Control Design of Detectable Periodic Markov Jump Systems

Abstract EN

An infinite horizon H 2 / 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-feedback H 2 / H ∞ control design is proposed.

It is shown that under the condition of detectability H 2 / H ∞ feedback gain can be constructed through the solution of a group of coupled periodic difference equations.