Smooth patchy control Lyapunov functions

Authors:
Rafal Goebel;Christophe Prieur;Andrew R. Teel
Affiliations:
Department of Mathematics and Statistics, Loyola University Chicago, 6525 N. Sheridan Rd., Chicago, IL 60626, USA;LAAS-CNRS, University of Toulouse, 7, avenue du Colonel Roche 31077 Toulouse, France;Department of Electrical and Computer Engineering, University of California Santa Barbara, CA 93106-9560, USA
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

A smooth patchy control Lyapunov function for a nonlinear system consists of an ordered family of smooth local control Lyapunov functions, whose open domains form a locally finite cover of the state space of the system, and which satisfy certain further increase or decrease conditions. We prove that such a control Lyapunov function exists for any asymptotically controllable nonlinear system. We also show a construction, based on such a control Lyapunov function, of a stabilizing hybrid feedback that is robust to measurement noise.