一类时变非线性振动系统的同步控制方法

对于一类非自治的非线性振动系统，设计了控制方法并建立了相应的派生系统，使得派生系统能与原系统达到同步.利用Lyapunov稳定性理论证明了两个系统在一定条件下可以达到同步，给出了耦合参数的选择条件.对于含参数激励与强迫激励的Mathieu方程以及拟周期激励的Duffing方程进行了实际的仿真计算，证明了派生系统可以与原系统的拟周期、混沌运动快速实现同步.关键词：派生系统同步差别方程

Synchronization of a class of time-varied nonlinear vibration system

For a class of nonautonomous nonlinear vibration system,a corresponding derived system is constructed.A novel control method to realize the synchronization between the derived and the original system is presented.The method is proved by Lyapunov stability theory.The principle for choosing coupling parameters is given.For a Mathieu system excited by parameters and external force,the simulation is carried out.The result shows that the derived system can achieve fast synchronization with the original system under the action of chaos.The simulation for Duffing system excited by quasi-periodic force shows that the derived system can reach synchronization with the original system under the quasi-periodic motion.