Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays

By Yurong Liu, Zidong Wang, Jinling Liang, Xiaohui Liu. IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics), 2008

513 citations recorded by the source corpus.

In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed discrete-time complex network with distributed delays is synchronized if certain linear matrix inequalities (LMIs) are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, for all admissible discrete and distributed delays, the dynamics of the estimation error is guaranteed to be globally asymptotically stable. Again, an LMI approach is developed for the state estimation problem. Two simulation examples are provided to show the usefulness of the proposed global synchronization and state estimation conditions. It is worth pointing out that our main results are valid even if the nominal subsystems within the network are unstable.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/87cbeaa28a7234676fbd05a82b0d33acab3e4c1e

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In Computer Networks and Communications

1. Zidong Wang
2. Huijun Gao
3. Xiaohui Liu
4. Jinling Liang
5. Yurong Liu
6. Bo Shen
7. Hongli Dong
8. Jun Hu

Citations in the corpus

• Global synchronization of complex dynamical networks with network failures (2010, unknown): “Lemma 2 ( Liu et al. [ 30 ] )”
• Recent Advances on Recursive Filtering and Sliding Mode Design for Networked Nonlinear Stochastic Systems: A Survey (2013, background): “The distributed time-delay in the discrete-time setting is an emerging concept that has been proposed in [30, 66] for complex networks.”
• Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays (2009, background): “Lemma 2 [23]: Let be a symmetric positivesemidefinite matrix, be a vector, and be scalars, where is a positive integer.”
• Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling (2012, background): “The nonlinear vector-valued function f : R → R is assumed to be continuous and satisfy the following sector-bounded condition [16]: [f(x)− f(y)− U1(x− y)] [f(x)− f(y)− U2(x− y)] ≤ 0 (2) for all x, y ∈ R, where U1 and U2 are constant matrices of appropriate dimensions.”
• Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays (2010, unknown): “Lemma 1 [19]: Let be a positive-semidefinite matrix, and .”