中文摘要：

研究离散非线性系统的倍周期分叉的分叉控制，设计线形控制器，非线性控制器以及状态反馈控制方法控制非线性动力系统。得到在控制前和控制后的分叉图，使系统的分叉达到预期的控制目的。根据实际的应用目的可以设计不同的控制器，其中线性控制器和非线性控制器由粗调和微调两部分组成。可以使系统分叉得到有效控制。选用的状态反馈控制器在适当选择控制器和有效的调控控制参数可以使分叉的效果控制达到良好的效果。

英文摘要：

This paper studies the control of period-doubling bifurcation of discrete nonlinear system, designs of linear controller and nonlinear controller, and state feedback control method to control nonlinear dynamical systems. The bifurcation diagrams before and after the control are obtained, so that the desired bifurcation control purposes of the system can be achieved. According to the purpose of actual application, different controllers can be designed. The linear controller and non-linear controller consist of two portions of rough tuning and fine tuning, so that bifurcation of the system can be controlled effectively. Selecting appropriate controller and effective control parameters, the state feedback can yield good results for the bifurcation control.