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Separable Lyapunov functions for monotone systems: Constructions and limitations.

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Author

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.

Publishing year

2015

Language

English

Pages

2497-2526

Publication/Series

Discrete and Continuous Dynamical Systems. Series B

Volume

20

Issue

8

Document type

Journal article

Publisher

Amer Inst Mathematical Sciences

Topic

  • Other Mathematics

Status

Published

Project

  • LCCC

Research group

  • LCCC

ISBN/ISSN/Other

  • ISSN: 1553-524X