Mixed H2/H∞-control of discrete-time Markovian jump linear systems

In this paper we consider the mixed H 2 /H∞-control problem for the class of discrete-time linear systems with parameters subject to Markovian jump linear systems (MJLS's). It is assumed that both the state variable and the jump variable are available to the controller. The transition probability matrix may not be exactly known, but belongs to an appropriate convex set. For this controlled discrete-time Markovian jump linear system, the problem of interest can be stated in the following way. Find a robust (with respect to the uncertainty on the transition Markov probability matrix) mean-square stabilizing state and jump feedback controller that minimizes an upper bound for the H 2 -norm, under the restriction that the H∞-norm is less than a prespecified value δ. The problem of the determination of the smallest H∞-norm is also addressed. We present an approximate version of these-problems via linear matrix inequality optimization.