Improved Results on Delay-dependent H∞ Control for Singular Time-delay Systems

The problem of delay-dependent H∞ control for singular systems with state delay is discussed. In terms of linear matrix inequality (LMI) approach, a delay-dependent bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free, and stable with H∞ performance condition via an augmented Lyapunov functional. Based on the BRL obtained, the delay-dependent condition for the existence of H∞ state feedback controller is presented via strict LMI. An explicit expression for the desired state feedback controller is also given. Numerical examples are presented to illustrate the significant improvement on the conservativeness of some reported results in the literature.