Stability analysis of nonlinear multiple time-delay systems with a periodic input

A dither is a high frequency signal introduced into a nonlinear multiple non-commensurate time-delay system in order to improve its performance. Stability of the nonlinear multiple non-commensurate time-delay system with a dither is deduced by establishing the stability of its corresponding relaxed model. If the relaxed model is stable, we can rigorously predict stability in finite time of the dithered multiple non-commensurate time-delay system, provided the frequency of the dither is high enough.