Calculating Floquet Multipliers for Periodic Solution of Non-smooth Dynamical System

Abstract

In this paper, we will discuss how to calculate Floquet multipliers of non-smooth dynamical systems which are continuous or discontinuous. The saltation matrix of discontinuous system plays an important role when computing the Floquet multipliers. In addition, a special periodic solution, semi-limit cycle, will be presented. We find that the stability of this periodic solution cannot be analyzed by the classical Floquet theory. More investigation is needed to enrich the theory of Floquet multipliers to non-smooth systems.