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Discrete and Continuous Dynamical Systems
Article . 2004 . Peer-reviewed
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Discrete and Continuous Dynamical Systems
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A constructive converse Lyapunov theorem on exponential stability

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2004 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete & Continuous Dynamical Systems - A, volume 10, pages 657-678 (issn: 1553-5231, Copyright policy )
Authors: Hafstein, Sigurdur Freyr;

doi: 10.3934/dcds.2004.10.657

A constructive converse Lyapunov theorem on exponential stability

Abstract

The paper is based on a software proposal for constructing candidate Lyapunov functions which are piecewise affine. These Lyapunov functions are interpolations on some grid points obtained by running the software based on linear programming. It is shown that, for a system whose equilibrium at the origin is exponentially stable, one may obtain a piecewise affine Lyapunov function by running the software (the run is \`\` successful'' or \`\` feasible''), i.e., an inversion of the Lyapunov theorem on exponential stability is given which allows the Lyapunov function to be obtained from a computer program. Some examples are given and comments on complexity are presented.

Keywords

Asymptotic stability in control theory, Numerical mathematical programming methods, exponential stability, software, Lyapunov and storage functions, Software, source code, etc. for problems pertaining to systems and control theory, converse theorems, linear programming, interpolations, Computational methods in systems theory, Lyapunov functions

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
47
Top 10%
Top 10%
Average
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