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

Abstract

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