基于一种新Lyapunov泛函方法的时滞复杂动态网络同步采样控制

Sampled-data synchronization of delayed complex dynamical networks based on a new Lyapunov functional method

本文针对时滞复杂动态网络同步采样控制问题进行研究。首先,构建时滞复杂动态网络模型和1个相关假设;其次,针对时滞复杂动态网络模型,基于Lyapunov-Krasovskii(L-K)稳定性分析理论和采样控制原理,建立新的Lyapunov泛函,这种Lyapunov泛函引入数据采样区间相关矩阵和优化双闭环泛函,从而能够更加充分利用系统的状态信息;最后,运用积分不等式方法构造Lyapunov泛函的导数,获得1个时滞复杂动态网络稳定的新判据并设计了1个保证时滞复杂动态网络同步的数据采样控制器。仿真研究结果表明:所给出的时滞复杂动态网络同步的充分条件是少保守性,且数据采样控制器是可行的。

The problem of a sampled-data synchronization of delayed complex dynamical networks is studied.Firstly, the delayed complex dynamical network model and a relate assumption are constructed. Secondly, based on the stability analysis theory of Lyapunov-Krasovskii(L-K) and the sampling control principle, a new Lyapunov functional is constructed, which introduced the correlation matrix of data sampling interval and an optimized double-closed loop functional to more fully obtain the state information of the system. At last, some newly reported integral inequalities are used to estimate the derivative of Lyapunov functional, a new criterion for stability of delayed complex dynamical networks is finally obtained, and a sampled-data controller is designed to ensure the synchronization of delayed complex dynamical networks.The results show that the sufficient conditions for the sampled-data synchronization of delayed complex dynamical networks are less conservative and the sampled-data controller is feasible.