Stability of nonsmooth dynamical systems

Abstract

This chapter starts with stability of various systems with state jumps: Lyapunov stability of Measure Differential Equations, vibro-impact systems, and impact oscillators. Then the so-called grazing bifurcations are introduced. The Lyapunov stability of complementarity Lagrangian mechanical systems is analyzed in detail, and it is shown how the Zhuravlev-Ivanov nonsmooth transformation introduced in Chap. 1 may be used for finite-time stabilization with a sliding-mode controller. The chapter ends with the analysis of Lyapunov stability of a simple system hitting a unilateral spring-like environment, and the use of copositive matrices for studying the stability of linear complementarity systems.