周期时变系统具有广泛的应用，如卫星姿态控制，直升机螺旋桨振动抑制等。由于该系统复杂的动态特性，很多分析控制问题目前仍然难以得到透彻的研究。而对于其近似系统的研究可以帮助解决周期时变系统中的难以处理的问题。相比于过去研究的周期分段定常系统，周期分段时变系统是周期时变系统的一种更高精度的近似系统，对于它的研究可更好地帮助了解周期时变系统，推广其工程应用。目前对于此系统的研究并不充分，基于此，本项目首先研究一种用周期分段时变系统逼近周期时变系统的近似方法。然后针对所获得的周期分段时变系统，分别研究子系统为线性时变及非线性时变情况下的系统稳定性及性能指标。进一步，针对周期分段线性时变和非线性时变系统，设计增益时变且易于工程应用的干扰抑制器。最后，基于所搭建的二自由度周期隔振台，设计含控制器的主动隔振装置并实验验证所得控制器的有效性。

The analysis and control of continuous-time periodic systems has attracted considerable attention due to their broad applications found in satellite attitude control, and helicopter blade vibration attenuation problems. The control problems involving continuous-time periodic systems are difficult to solve because of their intrinsic complicated dynamic characteristics. Compared with periodic piecewise constant system considered in previous research, periodic piecewise time-varying system represents an approximation system of continuous-time periodic system with higher fidelity. The investigation on periodic piecewise time-varying system will help understand the characteristics of continuous-time periodic system better and further promote its application. In this project, an approximation method of continuous-time periodic system with piecewise time-varying will be first proposed. Then periodic piecewise system with linear time-varying subsystems and nonlinear time-varying subsystems will be considered, and their stability and performance characterizations will be established. Moreover, disturbance attenuation controllers with time-varying gains will be designed. Finally, based on a 2-DOF periodic vibration isolation test rig, an active vibration isolation system with the synthesized controller will be employed to verify the effectiveness of the proposed method.