Asymptotic stabilization for a class of time-varying complex dynamical networks

Abstract

Asymptotic stabilization problem is investigated for a class of complex dynamical networks with the time-varying coupling configuration matrix and different nonlinear nodes. Firstly, a general time-varying complex dynamical network model with different nonlinear nodes and nonlinearly coupled functions is proposed. The time-varying outer coupling matrix in this paper is only needed to be dissipatively coupled, no matter its elements are negative or not and no matter it is symmetric or not. The outer coupling coefficients of the networks do not need to be known or continuous but need to be bounded. Based on Lyapunov stability theory and Barbalat's lemma and under the assumption that the bound of the time-varying coupling coefficients is uncertain, decentralized dynamical compensation controllers and the adaptive law are synthesized to stabilize the network asymptotically. When the bound of the time-varying coupling coefficients is known, the stabilization theorem is also proposed. Finally, a numerical example is presented to verify the effectiveness of our theoretical results.