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

This paper investigates the observer-based H∞H∞ control problem for a class of discrete-time mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete and distributed time-varying 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∞H∞ performance. Then a linear matrix inequality (LMI) approach for designing such an observer-based H∞H∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.