Stability certification of large scale stochastic systems using dissipativity

Ana Sofia Rufino Ferreira, Murat Arcak, Eduardo Sontag

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we analyse the stability of large-scale nonlinear stochastic systems, represented as an interconnection of lower-order stochastic subsystems. Stochastic stability in probability and noise-to-state stability are addressed, and sufficient conditions for the latter are provided. The method proposed proves network stability by using appropriate stochastic passivity properties of its subsystems, and the structure of its interactions. Stability properties are established by the diagonal stability of a dissipativity matrix, which incorporates information about the passivity properties of the systems and their interconnection. Next, we derive equilibrium-independent conditions for the verification of the relevant passivity properties of the subsystems. Finally, we illustrate the proposed approach on a class of biological reaction networks.

Original languageEnglish (US)
Pages (from-to)2956-2964
Number of pages9
JournalAutomatica
Volume48
Issue number11
DOIs
StatePublished - Nov 1 2012

Fingerprint

Stochastic systems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Keywords

  • Biochemical reactions
  • Large-scale systems
  • Networks and interconnections
  • Passivity
  • Stochastic stability

Cite this

Rufino Ferreira, Ana Sofia ; Arcak, Murat ; Sontag, Eduardo. / Stability certification of large scale stochastic systems using dissipativity. In: Automatica. 2012 ; Vol. 48, No. 11. pp. 2956-2964.
@article{d2f73e3847b446edb1bdce3c84147cc3,
title = "Stability certification of large scale stochastic systems using dissipativity",
abstract = "In this paper, we analyse the stability of large-scale nonlinear stochastic systems, represented as an interconnection of lower-order stochastic subsystems. Stochastic stability in probability and noise-to-state stability are addressed, and sufficient conditions for the latter are provided. The method proposed proves network stability by using appropriate stochastic passivity properties of its subsystems, and the structure of its interactions. Stability properties are established by the diagonal stability of a dissipativity matrix, which incorporates information about the passivity properties of the systems and their interconnection. Next, we derive equilibrium-independent conditions for the verification of the relevant passivity properties of the subsystems. Finally, we illustrate the proposed approach on a class of biological reaction networks.",
keywords = "Biochemical reactions, Large-scale systems, Networks and interconnections, Passivity, Stochastic stability",
author = "{Rufino Ferreira}, {Ana Sofia} and Murat Arcak and Eduardo Sontag",
year = "2012",
month = "11",
day = "1",
doi = "10.1016/j.automatica.2012.07.001",
language = "English (US)",
volume = "48",
pages = "2956--2964",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
number = "11",

}

Stability certification of large scale stochastic systems using dissipativity. / Rufino Ferreira, Ana Sofia; Arcak, Murat; Sontag, Eduardo.

In: Automatica, Vol. 48, No. 11, 01.11.2012, p. 2956-2964.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stability certification of large scale stochastic systems using dissipativity

AU - Rufino Ferreira, Ana Sofia

AU - Arcak, Murat

AU - Sontag, Eduardo

PY - 2012/11/1

Y1 - 2012/11/1

N2 - In this paper, we analyse the stability of large-scale nonlinear stochastic systems, represented as an interconnection of lower-order stochastic subsystems. Stochastic stability in probability and noise-to-state stability are addressed, and sufficient conditions for the latter are provided. The method proposed proves network stability by using appropriate stochastic passivity properties of its subsystems, and the structure of its interactions. Stability properties are established by the diagonal stability of a dissipativity matrix, which incorporates information about the passivity properties of the systems and their interconnection. Next, we derive equilibrium-independent conditions for the verification of the relevant passivity properties of the subsystems. Finally, we illustrate the proposed approach on a class of biological reaction networks.

AB - In this paper, we analyse the stability of large-scale nonlinear stochastic systems, represented as an interconnection of lower-order stochastic subsystems. Stochastic stability in probability and noise-to-state stability are addressed, and sufficient conditions for the latter are provided. The method proposed proves network stability by using appropriate stochastic passivity properties of its subsystems, and the structure of its interactions. Stability properties are established by the diagonal stability of a dissipativity matrix, which incorporates information about the passivity properties of the systems and their interconnection. Next, we derive equilibrium-independent conditions for the verification of the relevant passivity properties of the subsystems. Finally, we illustrate the proposed approach on a class of biological reaction networks.

KW - Biochemical reactions

KW - Large-scale systems

KW - Networks and interconnections

KW - Passivity

KW - Stochastic stability

UR - http://www.scopus.com/inward/record.url?scp=84867397605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867397605&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2012.07.001

DO - 10.1016/j.automatica.2012.07.001

M3 - Article

AN - SCOPUS:84867397605

VL - 48

SP - 2956

EP - 2964

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 11

ER -