Asymptotic stabilization of a class of smooth two-dimensional systems

This paper studies the asymptotic stabilizability of two-dimensional control systems. The class under consideration includes $C^\infty $-systems that satisfy a certain genericity assumption and all real analytic systems. Necessary and sufficient conditions for feedback stabilization using continuous...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 28; no. 6; pp. 1321 - 1349
Main Authors DAYAWANSA, W. P, MARTIN, C. F, KNOWLES, G
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1990
Subjects
Applied mathematics
Applied sciences
Computer science; control theory; systems
Control system synthesis
Control theory
Control theory. Systems
Exact sciences and technology
Neighborhoods
Asymptotic stability
Two dimensional system
Feedback
Necessary and sufficient condition
Stabilization
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Summary:This paper studies the asymptotic stabilizability of two-dimensional control systems. The class under consideration includes $C^\infty $-systems that satisfy a certain genericity assumption and all real analytic systems. Necessary and sufficient conditions for feedback stabilization using continuous feedback and a sufficient condition for $C^1 $-feedback stabilization are given. This latter condition is given in terms of an inequality involving two indices. If the direction of the inequality is changed, an obstruction to $C^\infty $-feedback stabilizability is obtained. A subclass of polynomial systems is also studied and given complete necessary and sufficient conditions for global asymptotic stabilization using $C^1 $-feedback.
ISSN:0363-0129
1095-7138
DOI:10.1137/0328070