Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

R. Rakkiyappan; B. Kaviarasan; Fathalla A. Rihan; S. Lakshmanan

doi:10.1016/j.jfranklin.2014.12.017

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

R. Rakkiyappan, B. Kaviarasan, Fathalla A. Rihan, S. Lakshmanan

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

Abstract

This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

Original language	English
Pages (from-to)	3178-3195
Number of pages	18
Journal	Journal of the Franklin Institute
Volume	352
Issue number	8
DOIs	https://doi.org/10.1016/j.jfranklin.2014.12.017
Publication status	Published - Aug 1 2015

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2014.12.017

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abstract = "This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.",

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AB - This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

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Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

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