Nonsmooth control-Lyapunov functions
- 19 November 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3 (01912216) , 2799-2805
- https://doi.org/10.1109/cdc.1995.478542
Abstract
It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional 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 nonsmooth case the theorem of Artstein (1983) relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A "nonstrict" version of the results, analogous to the LaSalle invariance principle, is also provided.Keywords
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