Contraction analysis of switched systems via regularization

David Fiore; S. John Hogan; Mario Di Bernardo

doi:10.1016/j.automatica.2016.06.028

Contraction analysis of switched systems via regularization

David Fiore
, S. John Hogan
, Mario Di Bernardo

Research output: Contribution to journal › Article (Academic Journal) › peer-review

39 Citations (Scopus)

453 Downloads (Pure)

Abstract

In this paper we study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that the conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.

Original language	English
Pages (from-to)	279-288
Number of pages	10
Journal	Automatica
Volume	73
Early online date	13 Sept 2016
DOIs	https://doi.org/10.1016/j.automatica.2016.06.028
Publication status	Published - Nov 2016

Research Groups and Themes

Engineering Mathematics Research Group
Bristol BioDesign Institute

Keywords

synthetic biology
regularization
contraction theory
incremental stability
switching controllers

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10.1016/j.automatica.2016.06.028

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://www.sciencedirect.com/science/article/pii/S0005109816302552. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 604 KBLicence: CC BY-NC-ND

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Emeritus Professor John Hogan
- S.J.Hoganbristol.acuk
- School of Engineering Mathematics and Technology - Emeritus Professor
Person: Honorary and Visiting Academic

Cite this

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title = "Contraction analysis of switched systems via regularization",

abstract = "In this paper we study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that the conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.",

keywords = "synthetic biology, regularization, contraction theory, incremental stability, switching controllers",

author = "David Fiore and Hogan, \{S. John\} and \{Di Bernardo\}, Mario",

year = "2016",

month = nov,

doi = "10.1016/j.automatica.2016.06.028",

language = "English",

volume = "73",

pages = "279--288",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Limited",

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TY - JOUR

T1 - Contraction analysis of switched systems via regularization

AU - Fiore, David

AU - Hogan, S. John

AU - Di Bernardo, Mario

PY - 2016/11

Y1 - 2016/11

N2 - In this paper we study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that the conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.

AB - In this paper we study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that the conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.

KW - synthetic biology

KW - regularization

KW - contraction theory

KW - incremental stability

KW - switching controllers

U2 - 10.1016/j.automatica.2016.06.028

DO - 10.1016/j.automatica.2016.06.028

M3 - Article (Academic Journal)

SN - 0005-1098

VL - 73

SP - 279

EP - 288

JO - Automatica

JF - Automatica

ER -

Contraction analysis of switched systems via regularization

Abstract

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Keywords

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Emeritus Professor John Hogan

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