Analysis of dither in relay feedback systems

Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal works by Zames and Shneydor (1976, 1977) and more recently by Mossaheb (1983) present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. This paper presents initial results on how to analyze and design dither in non smooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system obtained through an averaging approach. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the non smooth system.