Nonsmooth control-Lyapunov functions
Sontag, E.
Sussmann, H.J.
Dept. of Math., Rutgers Univ., New Brunswick, NJ ;
This paper appears in: Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Publication Date: 13-15 Dec 1995
Volume: 3,
On page(s): 2799-2805 vol.3
Meeting Date: 12/13/1995 - 12/15/1995
Location: New Orleans, LA, USA
ISBN: 0-7803-2685-7
References Cited: 11
INSPEC Accession Number: 5183603
Digital Object Identifier: 10.1109/CDC.1995.478542
Current Version Published: 2002-08-06
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
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