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Separable Lyapunov functions for monotone systems: Constructions and limitations.

In English

Författare

Summary, in English

For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum- and max-separable Lyapunov functions. One can be written as a sum, the other as a maximum of functions of scalar arguments. Several constructive existence results for both types are given. Notably, one construction provides a max-separable Lyapunov function that is defined at least on an arbitrarily large compact set, based on little more than the knowledge about one trajectory. Another construction for a class of planar systems yields a global sum-separable Lyapunov function, provided the right hand side satisfies a small-gain type condition. A number of examples demonstrate these methods and shed light on the relation between the shape of sublevel sets and the right hand side of the system equation. Negative examples show that there are indeed globally asymptotically stable systems that do not admit either type of Lyapunov function.

Publiceringsår

2015

Språk

Engelska

Sidor

2497-2526

Publikation/Tidskrift/Serie

Discrete and Continuous Dynamical Systems. Series B

Volym

20

Issue

8

Dokumenttyp

Artikel i tidskrift

Förlag

Amer Inst Mathematical Sciences

Ämne

  • Other Mathematics

Status

Published

Projekt

  • LCCC

Forskningsgrupp

  • LCCC

ISBN/ISSN/Övrigt

  • ISSN: 1553-524X