Convex robust H∞ control design to discrete-time systems with time-varying delay

Abstract

AbstractThe H∞ control of uncertain discrete-time systems with time varying delay affecting the state vector are investigated in this paper. The uncertainties are supposed polytopic and may affect all matrices of the system. Convex conditions expressed as linear matrix inequalities (LMIs) are proposed for the design of robust state feedback control gains that assures an H∞ guaranteed cost between the measured output and the exogenous input. These conditions are delay-dependent and are obtained by using parameter dependent Lyapunov-Krasovskii (L-K) functions and slack matrix variables that decouple the matrices of the system from the L-K function ones, yielding less conservative conditions. Crossed terms are tightly over bounded by means of Jensen's inequality. An extension based on following-model control design is proposed. A numerical example is presented to illustrate the efficacy of the proposal.