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Author Sontag, Eduardo ♦ Sussmann, Héctor J.
Source CiteSeerX
Content type Text
Publisher IEEE Publications
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Closed-loop Feedback Stabilization ♦ Generalized Derivative ♦ Optimal Control Technique ♦ Lasalle Invariance Principle ♦ Differential Inclusion ♦ Non-smooth Case ♦ Continuous Controllyapunov Function ♦ Control-lyapunov Function ♦ Viability Theory ♦ Set-valued Analysis ♦ Null Asymptotic Controllability ♦ Nonlinear Finitedimensional Control System ♦ Metric Space ♦ Various Name ♦ General Form ♦ Upper Contingent Derivative ♦ Clf Condition ♦ Non-strict Version ♦ Euclidean Space
Description Proc. IEEE Conf. Decision and Control
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...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1995-01-01