Stability analysis of dithered nonlinear singularly perturbed systems with time delays

A dither is a high frequency signal introduced into a nonlinear singular perturbed system, containing multiple noncommensurate time delays, in order to improve its performance. Stability of nonlinear singularly perturbed delay systems with a dither is analyzed by deriving its dithered reduced-order model and using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is high-enough. Moreover, stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed delay systems, provided the singular perturbation parameter is sufficiently small.<>