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.
KeywordsDirectional Derivative Differential Inclusion Nonlinear Control System Closed Convex Hull Viability Theory
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