General Classes of Control-Lyapunov Functions

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.

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