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

This paper deals with the problems of robust stability and stabilization for uncertain singular delay systems by using input-output approach other than traditional Lyapunovpsilas 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.