基于非线性观测器的一类分数阶混沌系统完全状态投影同步

基于分数阶系统稳定性理论，提出了用状态观测器来实现分数阶混沌系统完全状态投影同步的思想. 设计的状态观测器能够实现一类非线性分数阶系统的完全状态投影同步而不要求分数阶混沌系统是部分线性的，推广了投影同步的应用范围，且无需计算系统的条件Lyapunov指数. 另外，该方法理论严格，设计简单，能够达到任意比例因子的完全状态同步. 最后，利用该方法实现了分数阶Rssler系统的完全状态投影同步，数值仿真结果证实了它的有效性. 关键词： 分数阶 混沌系统 状态观测器 投影同步

Nonlinear observer based full-state projective synchronization for a class of fractional-order chaotic system

In this paper, based on the stability theory of the fractional-order system, an idea of using state observer to realize the full-state projective synchronization of fractional-order chaotic system is proposed. The designed observer can achieve full-state projective synchronization in a class of nonlinear fractional-order systems without the limitation of partial-linearity, extend the scope of application of projective synchronization, and does not require the calculation of the conditional Lyapunov exponents. In addition, this synchronization method is simple and theoretically rigorous, capable to achieve a full-state synchronization of arbitrary scaling factor. Finally, the method has been applied to realize the full-state projective synchronization of fractional-order Rssle system, and the simulation results verified the effectiveness of the method.