Control

Abstract

This chapter is concerned with the control problem for discrete-time switched systems with several typical switching signals. Firstly, the problem of designing $H_{\infty }$ state-feedback controllers is investigated for switched linear discrete-time systems with arbitrary switching and polytopic uncertainties. Two approaches on designing parameter-independent (robust) and parameter-dependent $H_{\infty }$ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities (LMIs). Then, considering the average dwell time (ADT) switching, an $\mu$-dependent approach is then introduced for the underlying systems to solve the $H_{\infty }$ controller , and the obtained conditions are dependent on the admissible increasing level $\mu$ of Lyapunov-like function values at switching instants. Finally, in a network-based environment, the quasi-time-dependent (QTD) $H_{\infty }$ control problem is investigated for a class of discrete-time switched linear systems with modal persistent dwell time (MPDT) switching. One redundant channel is introduced in the data transmission from sensor to controller to reduce the probabilities of packet dropouts occurred in the single channel case. Several examples are used to demonstrate the effectiveness of the developed theoretical results.