Dual LMI approach to linear positive system analysis

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6 Citations (Scopus)

Abstract

This paper is concerned with the dual-LMI-based analysis of linear positive systems. As the first contribution, we will show that the cerebrated Perron-Frobenius theorem can be proved concisely via a duality-based argument. On the other hand, in the second part of the paper, we extend the well-known result that a stable Metzler matrix admits a diagonal Lyapunov matrix as the solution of the Lyapunov inequality. More precisely, again via a duality-based argument, we will clarify a necessary and sufficient condition under which a stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries. This new result leads to an alternative proof for the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the L2 gain of positive systems.

Original languageEnglish
Title of host publicationICCAS 2012 - 2012 12th International Conference on Control, Automation and Systems
Pages887-891
Number of pages5
Publication statusPublished - Dec 1 2012
Externally publishedYes
Event2012 12th International Conference on Control, Automation and Systems, ICCAS 2012 - Jeju, Korea, Republic of
Duration: Oct 17 2012Oct 21 2012

Publication series

NameInternational Conference on Control, Automation and Systems
ISSN (Print)1598-7833

Conference

Conference2012 12th International Conference on Control, Automation and Systems, ICCAS 2012
CountryKorea, Republic of
CityJeju
Period10/17/1210/21/12

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All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Ebihara, Y. (2012). Dual LMI approach to linear positive system analysis. In ICCAS 2012 - 2012 12th International Conference on Control, Automation and Systems (pp. 887-891). [6393348] (International Conference on Control, Automation and Systems).