Synchronization of Singular Markovian Jumping Neutral Complex Dynamical Networks with Time-Varying Delays via Pinning Co
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NCHRONIZATION OF SINGULAR MARKOVIAN JUMPING NEUTRAL COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS VIA PINNING CONTROL∗ K. S. ANAND APS College of Engineering, Bangalore 560082, India
J. YOGAMBIGAI MMES College of Arts and Science, Melvisharam, Tamilnadu, India
G. A. HARISH BABU Reva Institute of Technology and Management, Bengaluru- 560064
M. SYED ALI Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu 632 115, India E-mail : [email protected]
S. PADMANABHAN RNS Institute of Technology, Channasandra, Bangalore 560098, India Abstract This article discusses the synchronization problem of singular neutral complex dynamical networks (SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach. By applying the Lyapunov stability theory, Jensen’s inequality, Schur complement, and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the stability of the system. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results. Key words
Singular complex networks; synchronization; Lyapunov-krasovski method; markovian jump; pinning control; linear matrix inequality
2010 MR Subject Classification
1
93D05; 93D20
Introduction
Over the past decade, complex networks have been studied intensively in various disciplines, such as sociology, biology, mathematics, and engineering [1–6]. A complex network is a large ∗ Received
August 29, 2018; revised July 4, 2019. The work of author was supported by NBHM grant. 2/48 (5)/2016/NBHMR.P)/- R -D II/ 14088
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ACTA MATHEMATICA SCIENTIA
Vol.40 Ser.B
set of interconnected nodes, where the nodes and connections can be anything, and a node is a fundamental unit having specific contents and exhibiting dynamical behavior. There are two ways of connection between nodes: directed connection and undirected connection, and the connection relationship can be unweighted and weighted. According to different ways of connection and whether there are weights or not between nodes, we get some different kinds of complex networks, such as undirected unweighted network, directed weighted network, etc. A complex network can exhibit complicated dynamics which may be absolutely different from that of a single node. The most well-known examples are electrical power grids, communication networks, internet, World Wide Web, metabolic systems, food webs, and so on. Hence, the investigation of complex dynamical networks is of great importance, and many systems in science and technology can be modeled as complex networks [8–10]. Time delay is encountered in many dynamical systems and often results in poor performance and even instability of control systems [11–13]. Because delay is usually time-varying in many practical system, many ap
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