Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systemswith time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskiifunction and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not onlyguarantees the regularity, causality, and exponential stability of the unforced system but also gives the correspondingestimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under theproposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuatorsaturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initialconditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numericalexamples are provided to illustrate the effectiveness of the proposed results