Delay-dependent robust stability and stabilization for uncertain singular system with time-varying delay

The problems of delay-dependent robust stability and stabilization for uncertain singular systems with time-varying delay are addressed in this paper. The uncertainty is assumed to be norm bounded. By establishing an integral inequality based on quadratic terms, a new delay-dependent robust stability criterion is derived and expressed in terms of linear matrix inequality (LMI). Based on the criterion, the problem of robust stabilization is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse-free and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Numerical examples are given to demonstrate the applicability and the less conservatism of the proposed method.