Stabilization of Nonlinear Singularly Perturbed Multiple Time-Delay Systems by Dither

Abstract

Dither is a high frequency signal injected into nonlinear systems for the purpose of improving their performance. Stability of the dithered nonlinear singularly perturbed multiple time-delay system is investigated by deriving its corresponding dithered reduced-order model and by using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is sufficiently high. Moreover, if the singular perturbation parameter is sufficiently small, then stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed multiple time-delay system.