混沌Lur′e系统基于时滞反馈PD控制的同步

Synchronization for Chaotic Lur′e Systems via Delayed Feedback PD Control

研究了混沌Lur′e系统同步的时滞反馈比例-微分(PD)控制器设计问题.系统中的非线性函数假设属于一个既有上界又有下界的扇形,这比相关文献中所使用的假设更具一般性.通过应用自由矩阵积分不等式来估计所构造的Lyapunov-Krasovskii泛函(LKF)的导数,提出了以一组线性矩阵不等式(LMIs)形式给出的同步判据,相应的控制器增益矩阵可以通过求解LMIs来获得,所得判据中不要求构造的LKF泛函中所有对称矩阵都正定.时滞Chua电路的数值仿真验证了该控制方法的有效性.

This paper deals with the synchronization problem of designing delayed feedback proportional-derivative(PD)controllers for chaotic Lur′e systems.The nonlinear function in the systems is assumed to belong to a sector that has both an upper bound and a lower bound,which is more general than those assumptions in the literature.By using a free-matrix-based integral inequality to estimate the derivative of the constructed Lyapunov-Krasovskii functional(LKF),a synchronization criterion was proposed in terms of linear matrix inequalities(LMIs)and the desired gain matrices can be obtained by solving the LMIs.This criterion does not require all the symmetric matrices involved in the LKF to be positive and definite.The numerical simulation of the delayed Chua′s circuit is given to verify the effectiveness of this method.