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Smooth patchy control Lyapunov functions |
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| Authors: | Rafal Goebel [Author Vitae] Christophe Prieur [Author Vitae] |
| Affiliation: | a Department of Mathematics and Statistics, Loyola University Chicago, 6525 N. Sheridan Rd., Chicago, IL 60626, USA b LAAS-CNRS, University of Toulouse, 7, avenue du Colonel Roche 31077 Toulouse, France c Department of Electrical and Computer Engineering, University of California Santa Barbara, CA 93106-9560, USA |
| 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. |
| Keywords: | Hybrid feedback Control Lyapunov function Nonlinear system Asymptotic controllability Asymptotic stability |
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