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

In this paper we consider the mixed H₂/H_∞ -control problem for the class of discrete-time linear systems with parameters subject to Markovian jumps. 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 appropriated 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 H₂ -norm, under the restriction that the H₂-norm is less than a pre-specified value δ. The problem of the determination of the smallest H_∞-norm is also addressed. We present an approximated version of these problems via linear matrix ineqaulity optimization