Abstract:

This paper discusses the quasi-synchronization problem in nonlinear heterogeneous complex dynamical networks with time-varying delays and sampled-data control with input-delay. The Lyapunov-Krasovskii functional with more information and the sampling interval delay information is constructed. Then, based on the Lyapunov-Krasovskii functional approach, integral inequality and linear matrix inequality method, by introducing a leader, sufficient criteria are obtained to guarantee quasi-synchronization for nonlinear heterogeneous dynamical networks. All heterogeneous followers can track the leader within a bounded range. And the upper bound of the quasi-synchronization error can be estimated. Simulation examples are provided to illustrate the theoretical results.

Key words: Lyapunov-Krasovskii functional, heterogeneous dynamical networks, quasi-synchronization, sampled-data control

摘要：

针对含时变时滞的非线性异质复杂网络，研究其在含输入时滞的采样控制下实现拟同步的问题。建立包含更多时滞信息以及采样间隔信息的Lyapunov-Krasovskii泛函，基于Lyapunov-Krasovskii稳定性理论、积分不等式方法和线性矩阵不等式方法，通过引入一个领导者获得了保证非线性异质复杂网络实现拟同步的充分条件。所有的异质跟随者都能在一个有界范围内追踪到领导者。并估计出实现拟同步的误差上界。通过数值仿真证明了理论结果的有效性。

关键词: Lyapunov-Krasovskii泛函, 异质动态网络, 拟同步, 采样控制