A separation principle for the H2-control of continuous-time infinite markov jump linear systems with partial observations

In this paper we devise a separation principle for the H₂ optimal control problem of continuous-time Markov jump linear systems with partial observations and the Markov process taking values in an infinite countable set S. We consider that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markov jump controller such that the closed loop system is stochastically 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 two sets of infinite coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other one associated with the optimal filtering problem. An important feature of our approach, not previously found in the literature, is to introduce an adjoint operator of the continuous-time Markov jump linear system to derive our results.