Persistence analysis of interconnected positive systems with communication delays

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Contribution to journalConference article

5 Citations (Scopus)

Abstract

This is a continuation of our preceding studies on the analysis of interconnected positive systems. Under mild conditions on positive subsystems and a nonnegative interconnection matrix, we showed that the state of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector. As a byproduct of this property, called persistence, it turned out that the output converges to the positive right eigenvector of the interconnection matrix. This result is effectively used in the formation control of multi-agent positive systems. The goal of this paper is to prove that the essential property of persistence is still preserved under arbitrary (time-invariant) communication delays. In the context of formation control, this preservation indicates that the desired formation is achieved robustly against communication delays, even though the resulting formation is scaled depending upon initial conditions for the state. From a mathematical point of view, the key issue is to prove that the delay interconnected positive system has stable poles only except for a pole of degree one at the origin, even though it has infinitely many poles in general. To this end, we develop frequency-domain (s-domain) analysis for delay interconnected positive systems.

Original languageEnglish
Article number7039684
Pages (from-to)1954-1959
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
Publication statusPublished - Jan 1 2014
Externally publishedYes
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

Fingerprint

Positive Systems
Communication Delay
Interconnected Systems
Persistence
Poles
Communication
Pole
Formation Control
Interconnection
Eigenvalues and eigenfunctions
Byproducts
Converge
Domain Analysis
Preservation
Eigenvector
Continuation
Multi-agent Systems
Frequency Domain
Subsystem
Initial conditions

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Persistence analysis of interconnected positive systems with communication delays. / Ebihara, Yoshio; Peaucelle, Dimitri; Arzelier, Denis.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039684, 01.01.2014, p. 1954-1959.

Research output: Contribution to journalConference article

Ebihara, Yoshio ; Peaucelle, Dimitri ; Arzelier, Denis. / Persistence analysis of interconnected positive systems with communication delays. In: Proceedings of the IEEE Conference on Decision and Control. 2014 ; Vol. 2015-February, No. February. pp. 1954-1959.
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