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

Abstract

In this paper, we study the problem of H ∞ 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 ∞ 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 ε, when ε is sufficiently small.