Control of singularly perturbed systems with Markovian jump parameters: anH-infinity approach

In this paper, we study the problem of H-infinity control for singularly pe rturbed linear continuous-time systems with Markovian jump parameters. The system under consideration is described by a state-space model, consisting of slow and fast dynamics with a continuous-time discrete-state Markov proc ess taking values on a finite set. On the basis of reduced-order technique, our attention is focused on the designing of state feedback control such t hat both stochastic stability and a prescribed H-infinity performance for t he full-order system are achieved. It has been shown that the above problem can be solved if a set of coupled Riccati equations has solution. Furtherm ore, the asymptotic structure of composite mode-dependent controller is cha racterized, which shows that the controller is independent of the singular perturbation epsilon, when epsilon is sufficiently small. (C) 1999 Elsevier Science Ltd. All rights reserved.