Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 23; no. 6; pp. 942 - 953
• Main Authors: Jinling Liang, Zidong Wang, Xiaohui Liu, Louvieris, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 2-D systems; Algorithms; Applied sciences; Arrays; Complex networks; Computer science; control theory; systems; Computer systems and distributed systems. User interface; coupling; Couplings; Dynamical systems; Exact sciences and technology; Information retrieval. Graph; Linear matrix inequalities; Mathematical analysis; Mathematical models; Networks; Nonlinear dynamics; Nonlinear dynamics and nonlinear dynamical systems; parameter uncertainties; Physics; Robustness; Software; Statistical physics, thermodynamics, and nonlinear dynamical systems; Studies; Synchronism; Synchronization; Synchronization ; coupled oscillators; Theoretical computing; Uncertain systems; Uncertain systems; Energy function; Kronecker product; State-space methods; Distributed system; complex networks; Synchronization; Fornasini-Marchesini model; coupling; Efficiency; 2-D systems; Non linear model; Discrete time; Complex network; parameter uncertainties; Modelling; Quadratic function
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2012.2193414

In this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini-Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.