Robust non-Zenoness of piecewise analytic systems with applications to complementarity systems

Abstract

This paper addresses non-Zenoness of a class of Lipschitz piecewise analytic systems subject to state perturbations and parameter uncertainties, motivated by sensitivity analysis of such systems. Specifically, the existence of uniform bounds on the number of mode switchings on a finite time interval is established for perturbed systems. For general parameterized piecewise analytic systems, this is achieved locally by extending Sussmann's result; this result is applied to a class of nonlinear complementarity systems arising from contact mechanics and constrained dynamical optimization. Furthermore, the existence of a global uniform bound on the number of switchings is established for bimodal piecewise affine systems by exploiting affine structure, under mild conditions on system parameters. It is shown that this bound is independent of initial state perturbations.