NDLI: Improving LaSalle's Invariance Principle using Geometric Clues

Content Provider	IEEE Xplore Digital Library
Author	Hyungbo Shim Jin Heon Seo
Copyright Year	2006
Description	Author affiliation: ASRI, Seoul Nat. Univ. (Hyungbo Shim; Jin Heon Seo)
Abstract	In this paper, we consider the stability properties of an equilibrium located at the boundary of an open forward invariant set. This is motivated by biological systems because they are nonnegative systems in nature and it is often the case that the equilibrium of interest has some zero component (so that it is at the boundary of the nonnegative orthant). Since the equilibrium is at the boundary, a non-isolated equilibrium can be asymptotically stable with respect to the positive orthant, which is emphasized in this paper. Then, we assert that some equilibrium at the boundary that is asymptotically stable in the usual sense does not admit a Lyapunov function, which may sound like a contradiction to the Lyapunov converse theorem. In fact, this is due to the non-uniform convergence rate around the boundary of forward invariant set. Inspired by the fact that some asymptotically stable equilibrium may not admit the Lyapunov function, we consider the well-known LaSalle's principle for proving the asymptotic stability. Since it turns out that it is not straightforward, we then provide a modified LaSalle's theorem, which incorporates the direction of vector fields around the boundary of forward invariant set
Starting Page	5253
Ending Page	5255
File Size	3549282
Page Count	3
File Format	PDF
ISBN	8995003847
DOI	10.1109/SICE.2006.315832
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-10-18
Publisher Place	South Korea
Access Restriction	Subscribed
Rights Holder	The Institute of Control, Automation and Systems
Subject Keyword	Forward contracts Lyapunov method Computer science Biological systems Convergence Asymptotic stability Nonlinear systems Systems biology Finance Chemistry Forward invariant set Positive systems LaSalle's principle Lyapunov function
Content Type	Text
Resource Type	Article

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