| General Classes Of Control-Lyapunov Functions (2007) | |||||||||||||||
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| . 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. 1. Introduction. In this paper, we study systems of the general form x(t) = f(x(t); u(t)) (1) where the states x(t) take values in a Euclidean space X= R n , the controls u(t) take values in a metric space U , and f is locally Lipschitz. A common approach for stabilization of this system to x = 0 relies on the use of abstract "energy" or "cost" functions that can be made to decrease in directions corresponding to ... | |||||||||||||||
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