MIXED H 2 / H ~ CONTROL OF DISCRETE-TIME MARKOVIAN JUMP LINEAR SYSTEMS *

In this paper we consider the mixed Hz/H~-control problem for the class of discrete-time linear systems with parameters subject to Markovian jumps (MJLS). It is assumed that both the state variable and the jump variable are available to the controller. The transition probability matxix 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 Hznorm, under the restriction that the H~ -norm is less than a pre-specified value $. The problem of the determination of the smallest H~ -norm is also addressed. We present an approximated version of these problems via LMI optimization.