Robust H∞ control for singular systems with state delay and parameter uncertainty

This paper considers the problem of robust H_∞ control for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. By using linear matrix inequality (LMI) approach, a sufficient condition is presented for a prescribed uncertain singular system with time-delay to have generalized quadratic stability and H_∞ performance. Furthermore, the design methods of state feedback controllers are considered such that the resulting closed-loop system has generalized quadratic stability with H_∞ performance. By means of LMIs, sufficient conditions are derived for the existence of memoryless and memorial static state feedback controllers, and the design methods for such controllers are provided in terms of the solutions of LMIs.