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

38 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

Access to Document

10.1016/j.jfranklin.2014.12.017

Cite this

@article{12225f67205f47bd8ac1838ce996ca72,

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

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.",

author = "R. Rakkiyappan and B. Kaviarasan and Rihan, {Fathalla A.} and S. Lakshmanan",

year = "2015",

month = aug,

day = "1",

doi = "10.1016/j.jfranklin.2014.12.017",

language = "English",

volume = "352",

pages = "3178--3195",

journal = "Journal of the Franklin Institute",

issn = "0016-0032",

publisher = "Elsevier Limited",

number = "8",

}

TY - JOUR

T1 - Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

AU - Rakkiyappan, R.

AU - Kaviarasan, B.

AU - Rihan, Fathalla A.

AU - Lakshmanan, S.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84922981811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922981811&partnerID=8YFLogxK

U2 - 10.1016/j.jfranklin.2014.12.017

DO - 10.1016/j.jfranklin.2014.12.017

M3 - Article

AN - SCOPUS:84922981811

VL - 352

SP - 3178

EP - 3195

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

SN - 0016-0032

IS - 8

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this