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Theoretical preliminaries

  • Isabelle Fantoni
  • Rogelio Lozano
Part of the Communications and Control Engineering book series (CCE)

Abstract

The purpose of this chapter is to present some definitions and background theory that will be used throughout this book. We will first introduce some important theorems based on Lyapunov theory. We will give some notions and basic concepts of passivity. Then, we will recall a necessary condition for the existence of a continuously stabilizing control law for non-linear systems, often referred to as Brockett’s necessary condition. The definitions of non-holonomic systems, underactuated systems and a homoclinic orbit are also given.

Keywords

Equilibrium Point Mobile Robot Homoclinic Orbit Holonomic Constraint Lyapunov Theory 
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.

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Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • Isabelle Fantoni
    • 1
  • Rogelio Lozano
    • 1
  1. 1.Heudiasyc, UMR CNRS 6599Universitè de Technologie de CompiègneCompiègneFrance

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