Stability and persistence analysis of large scale interconnected positive systems

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)


This paper is concerned with the analysis of large-scale interconnected systems constructed from positive subsystems and a nonnegative interconnection matrix. We first show that the interconnected system is admissible and stable if and only if a Metzler matrix built from the coefficient matrices of the positive subsystems and the interconnection matrix is Hurwitz stable. By means of this key lemma, we further provide several results that characterize the admissibility and stability of interconnected systems in terms of the weighted L1-induced norm of each positive subsystem and the Frobenius eigenvalue of the interconnection matrix. Moreover, in the case where every subsystem is SISO, we provide explicit conditions under which the interconnected system has the property of persistence, i.e., the state of the interconnected system converges to a unique strictly positive vector (up to a strictly positive constant multiplicative factor) irrespective of nonnegative and nonzero initial states. We illustrate the effectiveness of the persistence results via formation control of multi-agent systems.

Original languageEnglish
Title of host publication2013 European Control Conference, ECC 2013
PublisherIEEE Computer Society
Number of pages6
ISBN (Print)9783033039629
Publication statusPublished - 2013
Externally publishedYes
Event2013 12th European Control Conference, ECC 2013 - Zurich, Switzerland
Duration: Jul 17 2013Jul 19 2013

Publication series

Name2013 European Control Conference, ECC 2013


Other2013 12th European Control Conference, ECC 2013

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


Dive into the research topics of 'Stability and persistence analysis of large scale interconnected positive systems'. Together they form a unique fingerprint.

Cite this