$H_\infty$ and robust control of interconnected systems with Markovian jump parameters

In this paper, we examine the problems of stochastic stability and stabilization for a class of interconnected systems with Markovian jump parameters. The jumping parameters are treated as continuous-time, discrete- state Markov process. The purpose is to design a decentralized state feedback controller such that stochastic stability and a prescribed $H_\infty$-performance are guaranteed. Next, the robust $H_\infty$-control problem for linear interconnected systems with Markovian jump parameters and parametric uncertainties is studied. The parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state matrix. Both cases of finite-horizon and infinite-horizon are analyzed. We establish that the decentralized control problem for interconnected Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled differential (or algebraic) Riccati equations. Extension of the developed results to the case of uncertain jumping rates is provided.