Robust H-2-control for discrete-time Markovian jump linear systems

This paper deals with the robust H-2-control of discrete-time Markovian jum p linear systems. It is assumed that both the state and jump variables are available to the controller. Uncertainties satisfying some norm bounded con ditions are considered on the parameters of the system. An upper bound for the H-2-control problem is derived in terms of a linear matrix inequality ( 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 uncertainti es, the convex formulation considered in this paper imposes no extra condit ions than those in the usual dynamic programming approach. Finally some num erical examples are presented to illustrate the technique.