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Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization

Published online by Cambridge University Press:  11 August 2009

Iasson Karafyllis  and
Zhong-Ping Jiang
Iasson Karafyllis
Affiliation:
Department of Environmental Engineering, Technical University of Crete, 73100 Chania, Greece. [email protected]
Zhong-Ping Jiang
Affiliation:
Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, NY 11201, USA. [email protected]
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Abstract

In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF) method and can be applied to very general nonlinear time-varying systems with disturbance and control inputs, including both finite and infinite-dimensional systems. The generality of the proposed methodology is also reflected upon by the fact that partial stability with respect to output variables is addressed. In addition, it is shown that the generalized CLF method can lead to a novel tool for the explicit design of robust nonlinear controllers for a class of time-delay nonlinear systems with a triangular structure.

Keywords

Control Lyapunov Functionstabilizationtime-varying systemsnonlinear control
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 887 - 928
Copyright
© EDP Sciences, SMAI, 2009

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