Control of singularly perturbed systems with Markovian jump parameters:: an H∞ approach

In this paper, we study the problem of H(infinity) control for singularly perturbed 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 process 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 that both stochastic stability and a prescribed H(infinity) performance for the 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. Furthermore, the asymptotic structure of composite mode-dependent controller is characterized, 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.