General Classes of Control-Lyapunov Functions

  • Eduardo D. Sontag
  • Héctor J. Sussmann
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)


The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov functions (CLF’s) defined by means of generalized derivatives. In this manner, one obtains a complete characterization of asymptotic controllability, applying in principle to a far wider class of systems than Artstein’s Theorem (which relates closed-loop feedback stabilization to the existence of smooth CLF’s). The proof relies on viability theory and optimal control techniques.


Directional Derivative Differential Inclusion Nonlinear Control System Closed Convex Hull Viability Theory 
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Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • Eduardo D. Sontag
    • 1
  • Héctor J. Sussmann
    • 2
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Dept. of MathematicsRutgers UniversityNew BrunswickUSA

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