Uniting Two Control Lyapunov Functions for Affine Systems

The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient...

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Bibliographic Details
Published in2008 47th IEEE Conference on Decision and Control Vol. 55; no. 8; pp. 1923 - 1927
Main Authors Andrieu, V, Prieur, C
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.08.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Applied sciences
Asymptotic properties
Automatic
Automatic control
Computer science; control theory; systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Controllability
Engineering Sciences
Exact sciences and technology
Feedback control
Instruments
Lyapunov functions
Lyapunov method
Lyapunov stabilization
Mathematical models
Modelling and identification
Nonlinear control systems
Nonlinear systems
Optimal control
Origins
Stability
State feedback
Sufficient conditions
uniting problems
State feedback
Second order equation
Compact space
uniting problems
Control program
Lyapunov stabilization
Non linear control
Non linear system
Affine transformation
nonlinear systems
Optimal control
Global stabilization
Controllability
Asymptotic approximation
Lyapunov function
Uniting
Lyapunov design
Stabilization
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ISSN0018-9286
1558-2523
DOI10.1109/TAC.2010.2049689

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Summary:The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2049689