H∞ control of linear singular time-delay systems subject to impulsive perturbations

This study addresses the problem of H∞ control for linear singular time-delay systems subject to impulsive perturbations. Specifically, the impulses are allowed to be destabilising, i.e. they may degrade the closed-loop performance of the considered systems. With the aid of a descriptor-type impulse-time-dependent Lyapunov functional, a sufficient condition for the solvability of the problem is derived in terms of linear matrix inequalities (LMIs). By solving a set of LMIs, a desired state-feedback controller is found, which guarantees that the closed-loop system is impulse-free, internally exponentially stable, and achieves a prescribed L2 -gain. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed method.