Input-output approach to robust stability and stabilization for singular delay systems

Abstract

This paper deals with the problems of robust stability and stabilization for uncertain singular delay systems by using input-output approach other than traditional Lyapunov’s second method. Based on the small gain theorem, the notion of input-output stability is first developed. Then a delay-dependent robust stability criterion in terms of strict linear matrix inequality (LMI) is derived to verify that the singular delay system is regular, impulse free as well as input-output stable (also asymptotically stable) for all admissible uncertainties. Next, we have also proposed a method for designing a linear state feedback controller such that the closed-loop system is robustly stable. Finally, a numerical example is proposed to illustrate the effectiveness of the obtained results.