Robust stability and stabilization for uncertain singular time-delay systems via discretized Lyapunov functional approach

Abstract

This paper considers the problems of robust stability and stabilization for uncertain singular systems with time delay. A singular-type complete quadratic Lyapunov-Krasovskii functional (LKF) is introduced, which combines the discretization LKF method to give the linear matrix inequality (LMI) condition for the singular time-delay system to be regular, impulse free and asymptotically stable. The free weighting matrix approach contributes to decouple the system matrices from the Lyapunov function matrices. Based on the stability criterion, the robust stabilization problem is studied. Numerical examples are provided to demonstrate the application of the proposed method.