基于采样控制和输入饱和的不确定复杂网络同步研究

Synchronization of Uncertain Complex Networks with Sampled-data and Input Saturation

在实际网络系统中,广泛存在外部的干扰、参数波动等不确定现象,会导致系统无法实现同步,甚至会破坏系统的稳定性。因此研究不确定复杂动态网络的同步问题具有重要的意义。针对一类非线性不确定复杂动态网络,文中研究其在采样控制和输入饱和的条件下实现同步的问题。首先,建立非线性不确定复杂动态网络模型,其次通过引入一个领导者,设计了包含输入饱和的采样控制协议。然后构造合适的时间依赖Lyapunov函数,通过运用稳定性理论、积分不等式方法和线性矩阵不等式方法,证明了非线性不确定复杂动态网络在一定条件下可以实现同步,即每个跟随者最终都能追踪到领导者,并给出了实现同步的充分判据。最后,通过数值仿真验证了所得理论结果的正确性和有效性。

In actual network systems,there are widespread external interference and parameter mutations and other uncertain phenomena,which will cause the system to fail to achieve synchronization,and even destroy the stability of the system.Therefore,it is important to study uncertain complex networks.This paper discusses the synchronization problem of nonlinear uncertain complex dynamical networks with sampled-data and input saturation.Firstly,we establish a nonlinear and uncertain complex network model.Secondly,a leader is introduced to design a sampled-data control protocol with input saturation.By constructing an appropriate time-dependent Lyapunov functional and applying the stability theory,integral inequality method and the linear matrix inequality method,it is proved that the nonlinear uncertain complex dynamical networks can achieve synchronization under certain conditions,that is every follower can track the leader,and the sufficient criteria for achieving synchronization of nonlinear uncertain complex networks is derived.Finally,simulation examples are provided to verify the effectiveness and validity of the theoretical results.