Structural stabilization and quenching by dither in nonlinear systems

A dither is a high frequency signal introduced into a nonlinear system for the purpose of augmenting stability or quenching undesirable jump-phenomena. In an earlier paper [2], it had been shown that the effects of a dither depend on its amplitude distribution function. The stability of a dithered system was related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity. In this paper, which is a continuation of [2], the ability of dithers to quench jump-phenomena (i.e., to induce continuity) is demonstrated. A notion of structural-stability for feedback equations is introduced, and it is shown that dithers can structurally stabilize large classes of nonlinear systems subject to a second-order Lipschitz condition. The quenching properties of dithers are explained in terms of an effective narrowing of the nonlinear incremental sector.