# 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

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topKarafyllis, 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 -

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