The separation principle for the H2-control of discrete-time Markovian jump linear systems

In this paper we consider the H₂ control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from 2 coupled algebraic Riccati equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems.