Quantised robust H<inf>∞</inf> output feedback control of discrete-time systems with random communication delays

Abstract

In this paper a stability criterion and robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> mode delay dependent quantised dynamic output feedback controller design problem for discrete time systems with random communication delays, packet dropouts and quantisation errors are investigated. Random communication delays from sensor to controller network are modelled using a finite state Markov chain with a special transition probability. A logarithmic quantiser is used to quantise the measured output. Lyapunov-Krasovskii (L-K) functional approach is employed to derive the stochastic stability criterion for the system with a given attenuation level. Sufficient conditions for the existence of an output feedback controller is formulated in terms of bilinear linear matrix inequalities (BMIs). Due to the special transition probability matrix, a new slack matrix is added to BMIs to relax the sufficient conditions for the existence an output feedback controller. Furthermore, an iterative algorithm is used to convert the BMIs into quasi-convex optimization problem which can be solved easily.