Robust H2-control for discrete-time Markovian jump linear systems

This paper deals with the robust H-2-control of discrete-time Markovian jump linear systems. Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upperbound for the H-2-control problem is derived in terms of an LMI optimization problem. For the case in which there are no uncertainties, we show that the convex formulation is equivalent to the existence of the mean square stabilizing solution for the set of coupled algebraic Riccati equations arising on the quadratic optimal control problem of discrete-time Markovian jump linear systems. Therefore, for the case with no uncertainties, the convex formulation considered in this paper imposes no extra conditions than those in the usual dynamic programming approach.