Exponential stability of singularly perturbed discrete systems with time-delay

Abstract

In this paper, the exponential stability of singularly perturbed discrete systems (SPDSs) with time-delay is investigated via the Lyapunov's direct method. In the previous results about the SPDS with time-delay, the asymptotic stability is obtained using the frequency-domain approach. However, we propose a composite Lyapunov function to show that the SPDS with time-delay is exponentially stable with the decay rate γ. In terms of the LMI, the sufficient condition for the exponential stability of the linear SPDS is presented. Moreover, based on the linear SPDS result, the exponential stability of the nonlinear SPDS with time-delay is also considered. Finally, numerical examples are given to validate the proposed results.