Separable Lyapunov functions for monotone systems

Anders Rantzer, Björn Rüffer, Gunther Dirr

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

Abstract

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.
DOIs
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control, 2013 - Florence, Italy
Duration: 2013 Dec 102013 Dec 13
Conference number: 52
http://www.ieeecss.org/CAB/conferences/cdc2013/

Conference

Conference52nd IEEE Conference on Decision and Control, 2013
Abbreviated titlecdc2013
Country/TerritoryItaly
CityFlorence
Period2013/12/102013/12/13
Internet address

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • stability
  • Lyapunov functions
  • monotone systems

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  • LCCC

    Holmqvist, A. (Researcher), Andersson, N. (Researcher), Cervin, A. (Researcher), Mannesson, A. (Researcher), Gattami, A. (Researcher), Ghulchak, A. (Researcher), Papadopoulos, A. V. (Researcher), Rantzer, A. (Researcher), Robertsson, A. (Researcher), Sootla, A. (Researcher), THEORIN, A. (Researcher), Bernhardsson, B. (Researcher), Olofsson, B. (Researcher), Wittenmark, B. (Researcher), Grussler, C. (Researcher), Johnsson, C. (Researcher), MADJIDIAN, D. (Researcher), Johannesson, E. (Researcher), Magnusson, F. (Researcher), Ståhl, F. (Researcher), Como, G. (Researcher), Chasparis, G. (Researcher), Turesson, G. (Researcher), Dressler, I. (Researcher), Åkesson, J. (Researcher), Cho, J. H. (Researcher), Årzén, K.-E. (Researcher), Åström, K. J. (Researcher), Sou, K. C. (Researcher), Mårtensson, K. (Researcher), Berntorp, K. (Researcher), Soltesz, K. (Researcher), Lessard, L. (Researcher), Hast, M. (Researcher), Rönn, M. (Researcher), Ansbjerg Kjær, M. (Researcher), Maggio, M. (Researcher), Kristalny, M. (Researcher), Garpinger, O. (Researcher), From, P. J. (Researcher), Larsson, P.-O. (Researcher), Giselsson, P. (Researcher), Johansson, R. (Researcher), Hägglund, T. (Researcher), Vladimerou, V. (Researcher), Romero Segovia, V. (Researcher), Aurelius, A. (Researcher), Cedersjö, G. (Researcher), Bür, K. (Researcher), Dellkrantz, M. (Researcher), Du, M. (Researcher), Amani, P. (Researcher), Larsson, R. (Researcher), Tärneberg, W. (Research student), Li, Z. (Researcher), Yin, L. (Researcher), Tufvesson, F. (Researcher), Höst, S. (Researcher), Nilsson, B. (Researcher), Stenström, S. (Researcher), Andersson, J. A. (Researcher), Diehl, S. (Researcher), Dürango, J. (Researcher), Ghazaei Ardakani, M. (Researcher), Forsberg, P.-O. (Researcher), Bengtsson, F. (Researcher), Jörntell, H. (Researcher), Arévalo, C. (Researcher), Führer, C. (Researcher), Andersson, C. (Researcher), Mohammadi, F. (Researcher), Ödling, P. (Researcher), Andersson, M. (Researcher), Kihl, M. (Researcher) & Tunestål, P. (Researcher)

    2008/07/012018/06/30

    Project: Research

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