Delay-dependent robust stability criterion and robust stabilization for uncertain singular time-delay systems

In this paper, the delay-dependent robust stability criterion and robust stabilization for singular time-delay systems with norm-bounded parametric uncertainty is investigated. First, in terms of the Lyapunov technique and linear matrix inequalities (LMIs), a delay-dependent stability criterion for the nominal singular time-delay system is established, which guarantees the system to be regular, impulse free and asymptotically stable. Then, based on the concept of generalized quadratic stabilization, the problem of robust stabilization for the uncertain singular time-delay systems is solved via state feedback, which guarantees the closed-loop system to be regular, impulse free and asymptotically stable for all admissible uncertainties. The explicit expression for the desired robustly stabilizing controller is given by using the LMIs and the cone complementarity linearization iterative algorithm.