Title :
Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks
Author :
Jinling Liang ; Zidong Wang ; Xiaohui Liu ; Louvieris, Panos
Author_Institution :
Dept. of Math., Southeast Univ., Nanjing, China
fDate :
6/1/2012 12:00:00 AM
Abstract :
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.
Keywords :
discrete time systems; nonlinear control systems; robust control; state-space methods; synchronisation; 2D complex network model; 2D discrete-time coupled dynamical networks; 2D nonlinear state space model; Fornasini-Marchesini second model; Kronecker product; energy-like quadratic function; global synchronization; robust synchronization; Arrays; Complex networks; Couplings; Linear matrix inequalities; Robustness; Synchronization; Uncertain systems; 2-D systems; complex networks; coupling; parameter uncertainties; synchronization;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2012.2193414