Copyright © 2012 Jinxing Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems
with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii
function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only
guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding
estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the
proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator
saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial
conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical
examples are provided to illustrate the effectiveness of the proposed results.