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Smooth patchy control Lyapunov functions
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DOI：10.1016/j.automatica.2008.10.023.png)
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Abstract
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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. (C) 2008 Elsevier Ltd. All rights reserved.
Keywords:
Hybrid feedback
Control Lyapunov function
Nonlinear system
Asymptotic controllability
Asymptotic stability
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