Exponential synchronization of complex networks with Markovian jump and mixed delays
By Yurong Liu, Zidong Wang, Xiaohui Liu. 2008
172 citations recorded by the source corpus.
In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.
Subfields: Computer Networks and Communications, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/0af7beeaf04f145f8a038b2045a4775a323ef952
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In Computer Networks and Communications
- Zidong Wang
- Jinling Liang
- Xiaohui Liu
- Yurong Liu
- Yingchun Wang
- Huaguang Zhang
- Xing-yuan Wang
- Dongsheng Yang
In Molecular Biology
Citations in the corpus
- Networked Synchronization Control of Coupled Dynamic Networks With Time-Varying Delay (2010, background): “The stochastic coupling and disturbances were considered for the general delayed discrete-time networks in [6].”
- Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays (2010, unknown): “Suchageneraldescriptionhas been exploited in a number of papers, e.g., [ 18 ] and [19].”
- Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays (2008, background): “Very recently, in [22], the synchronization problem has been investigated for coupled networks with both discrete and distributed time delays.”