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Stability of Nonsmooth Dynamical Systems

  • Bernard BrogliatoEmail author
Chapter
Part of the Communications and Control Engineering book series (CCE)

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.

Keywords

Contact Force Lyapunov Function Differential Inclusion Lyapunov Stability Periodic Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

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