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Separable Lyapunov functions for monotone systems

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Author

Summary, in English

Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max- separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.

Publishing year

2013

Language

English

Publication/Series

IEEE Xplore Digital Library

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Control Engineering

Keywords

  • stability
  • Lyapunov functions
  • monotone systems

Conference name

52nd IEEE Conference on Decision and Control, 2013

Conference date

2013-12-10 - 2013-12-13

Conference place

Florence, Italy

Status

Published

Project

  • LCCC

Research group

  • LCCC