Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization

Iasson Karafyllis; Zhong-Ping Jiang

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 4, page 887-928
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Karafyllis, Iasson, and Jiang, Zhong-Ping. "Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 887-928. <http://eudml.org/doc/250755>.

@article{Karafyllis2010,
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. },
author = {Karafyllis, Iasson, Jiang, Zhong-Ping},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control Lyapunov Function; stabilization; time-varying systems; nonlinear control; control Lyapunov function; time-varying systems},
language = {eng},
month = {10},
number = {4},
pages = {887-928},
publisher = {EDP Sciences},
title = {Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization},
url = {http://eudml.org/doc/250755},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Karafyllis, Iasson
AU - Jiang, Zhong-Ping
TI - Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 887
EP - 928
AB - 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.
LA - eng
KW - Control Lyapunov Function; stabilization; time-varying systems; nonlinear control; control Lyapunov function; time-varying systems
UR - http://eudml.org/doc/250755
ER -

References

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