Observer-Based H∞ Control of Uncertain Singular Systems with Time-Varying Delay

This paper is devoted to the problem of robust H-infinity control for a class of uncertain singular systems with time-varying delay and norm-bounded parameter uncertainties. The states of the singular system are unmeasured. A state feedback controller based on an observer is proposed. The observer system is singular and with the same dimension as that of the given singular system. By employing free-weighting matrix and linear matrix inequality (LMI) approach, a new stability criterion for the nominal and unforced singular system is obtained. Based on this criterion, a delay-dependent sufficient condition is given to ensure that there exists an observer-based state feedback stabilizing controller such that the augmented closed-loop system is regular, impulse free and stable with the prescribed H-infinity performance level for all admissible parameter uncertainties, and the corresponding design algorithm of observer and controller is proposed. A numerical example is included to show the effectiveness of the proposed method.