Delay-dependent robust H∞ stability and stabilization for uncertain singular system

This paper investigates the problem of delay-dependent robust H_infin control for uncertain singular systems with time-varying state delay. The considered systems are not necessarily assumed to be regular and causal. In terms of linear matrix inequality (LMI)approach, a delay-dependent stabilizable criterion is given to ensure the nominal system to be regular, impulse-free and stable. Based on the criterion, the problem mentioned above is solved via state feedback controller, which guarantees that, for all admissible uncertainties, the closed-loop system is not only regular, causal and stable, but also satisfies a prescribed H_infin performance condition. Some numerical examples are provided to demonstrate the efficiency and less conservition of the proposed methods in this paper.