Averaging of Nonsmooth Systems Using Dither

It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency dither signal of a quite arbitrary shape can be used tonarrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearitiesof feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and hasbounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.