Robust Synchronization for Multistable Systems

Hafiz Ahmed; Rosane Ushirobira; Denis  Efimov; Wilfrid  Perruquetti

doi:10.1109/TAC.2015.2476156

Robust Synchronization for Multistable Systems

Hafiz Ahmed, Rosane Ushirobira, Denis Efimov, Wilfrid Perruquetti

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Abstract

In this note, we study a robust synchronization problem for multistable systems evolving on manifolds within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems, a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant set is assumed to admit a decomposition without cycles, that is, with neither homoclinic nor heteroclinic orbits. Numerical simulation examples illustrate our theoretical results.

Original language	English
Pages (from-to)	1625-1630
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	61
Issue number	6
Early online date	2 Sept 2015
DOIs	https://doi.org/10.1109/TAC.2015.2476156
Publication status	Published - Jun 2016

Bibliographical note

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Keywords

Syncronization
Robustness
Lyapunov methods
Stability analysis
Nonlinear systems
Manifolds
Numerical stability
robust control
syncronisation
robust synchronization protocol
multistable systems
input-to-state stability framework
ISS framework

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Cite this

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title = "Robust Synchronization for Multistable Systems",

abstract = "In this note, we study a robust synchronization problem for multistable systems evolving on manifolds within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems, a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant set is assumed to admit a decomposition without cycles, that is, with neither homoclinic nor heteroclinic orbits. Numerical simulation examples illustrate our theoretical results.",

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AU - Ushirobira, Rosane

AU - Efimov, Denis

AU - Perruquetti, Wilfrid

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KW - Syncronization

KW - Robustness

KW - Lyapunov methods

KW - Stability analysis

KW - Nonlinear systems

KW - Manifolds

KW - Numerical stability

KW - robust control

KW - syncronisation

KW - robust synchronization protocol

KW - multistable systems

KW - input-to-state stability framework

KW - ISS framework

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M3 - Article

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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Robust Synchronization for Multistable Systems

Abstract

Bibliographical note

Keywords

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