Robust Stability Analysis of Discrete Uncertain Singularly Perturbed Time-Delay Systems

In this paper, we investigate the robust stability problem of a class of LTI discrete uncertain singularly perturbed time-delay systems. If the singular perturbation parameter of these systems is sufficiently small, they can be separated into two reduced-order subsystems, the slow subsystem and fast subsystem. Two stability criteria for the slow and fast subsystem of the uncertain system are then derived respectively. Then, the robust asymptotic stability of the full-order uncertain system subject to structured perturbations can be investigated from those of the uncertain slow and fast subsystems