时滞动态复杂网的同步反馈控制

复杂网络的研究已经渗透到许多科学领域,从物理学、生物神经学到工程学与社会科学等都有着重要的应用.在实际网络中,节点很有可能存在时间滞后,因此,本文引入了一类时滞动态复杂网的模型,并且研究了它的同步特性.假设存在一个不稳定的固定点,分别采用时滞反馈控制和标准反馈控制,首先得到系统的误差方程,然后应用线性矩阵不等式(LMI)方法,基于李亚普诺夫稳定性定理,给出了误差方程稳定的充分条件.数值举例和仿真结果显示误差系统逐渐趋于稳定.

Synchronization feedback control of time-delay complex dynamical networks

Complex networks have been intensively studied in many fields,from physics and neurobiology to engineering and social sciences. In this paper,aiming at the time-delay property of network,a more general time-delay dynamical network model was presented. After an unstable fixed point was supposed to be existed,we adopted the time-delay feedback control method and the standard feedback control method to acquire the error of the system,which can be described by a linear matrix inequality (LMI) in terms of a parameter matrix associated with network. Then the sufficient and necessary condition of the stability of the matrix was presented,according to Lyapunov theorem. Finally,a numerical simulation example is provided to verify the theoretical results.