Robust H∞ control for uncertain linear time-delay singularly perturbed systems

The problem of robust H_∞ control problem for a class of uncertain linear time-delay singularly perturbed systems is considered. Based on the Lyapunov-Kravoskii and linear matrix inequality approach, a bounded real lemma is obtained for the considered linear time-delay singularly perturbed system to be stable with disturbance attenuation level less than a given bound for perturbed parameter ε ∈ (0, ε*]. The robust H_∞ performance analysis and robust H_∞ controller synthesis problems are also solved. Two numerical examples are given to illustrate the applicability of the proposed approach.