Observer-based H∞ control of discrete Markovian jump delay systems with random packet losses and multiplicative noises

Abstract

This paper investigates the observer-based H∞ control problem for a class of mixed-delay Markovian jump systems with random communication packet losses and multiplicative noises. The mixed delays comprise both discrete time-varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based feedback controller are derived such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H∞ performance. Then, a linear matrix inequality approach for designing such an observer-based H ∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.