Decentralised Variable Structure Control for Time Delay Interconnected Systems

A class of multiple time varying delay interconnected systems with nonlinear disturbances is considered in this Chapter, where both the known and uncertain interconnections involve time delay. A decentralised static output feedback variable structure control is synthesised, which is independent of the time delays, to stabilise the system globally uniformly asymptotically. The stability of the closed loop system is analysed based on the Lyapunov Razumikhin approach. Then, for interconnected systems where each subsystem is square, it is shown that the effects of the uncertain interconnections can be largely rejected by appropriate controllers if the delays are known and the uncertain interconnections are bounded by a class of functions of the outputs and delayed outputs. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.