Separable Lyapunov functions for monotone systems

Anders Rantzer, Björn Rüffer, Gunther Dirr

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

16 Citations (SciVal)


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.
Original languageEnglish
Title of host publicationIEEE Xplore Digital Library
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control, 2013 - Florence, Italy
Duration: 2013 Dec 102013 Dec 13
Conference number: 52


Conference52nd IEEE Conference on Decision and Control, 2013
Abbreviated titlecdc2013
Internet address

Subject classification (UKÄ)

  • Control Engineering


  • stability
  • Lyapunov functions
  • monotone systems


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