| Nonsmooth Control-Lyapunov Functions (1995) | |||||||||||||||||
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| It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional 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. 1. Introduction We deal with 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 widely used technique for stabilization of thi... | |||||||||||||||||
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