Stability of Nonsmooth Dynamical Systems

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


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.


Contact Force Lyapunov Function Differential Inclusion Lyapunov Stability Periodic Trajectory 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

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