Nonsmooth control-Lyapunov functions

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It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in set-valued analysis and the theory of differential inclusions with various names such as 'upper contingent derivative.' This result generalizes to the non-smooth case the theorem of Artstein relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A 'non-strict' version of the results, analogous to the LaSalle Invariance Principle, is also provided.

Original languageEnglish (US)
Pages (from-to)2799-2805
Number of pages7
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1995
EventProceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA
Duration: Dec 13 1995Dec 15 1995

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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