线性时变周期系统的能控性与能稳定性问题

Journal of Systems Engineering and Electronics ›› 2010, Vol. 32 ›› Issue (4): 812-815.

线性时变周期系统的能控性与能稳定性问题

张雪峰，张庆灵

（东北大学理学院, 辽宁沈阳 110004）

出版日期:2010-04-23 发布日期:2010-01-03

Problem on controllability and stabilizability of linear time-varying periodic system

ZHANG Xue-feng, ZHANG Qing-ling

（School of Sciences, Northeastern Univ., Shengyang 110004, China）

Online:2010-04-23 Published:2010-01-03

摘要/Abstract

摘要：

线性时变周期系统是一类普遍存在的重要而又研究较少的系统。介绍了线性时变周期系统的几种应用实例，给出了两种判定时变周期系统能控性与能观性的必要条件，该判别条件的优点是不必计算系统的状态转移矩阵，使判别时变周期系统能控性与能观性简单、高效、易于实现。讨论了时变周期系统在状态反馈下的能稳定性问题，得到了类似于线性定常系统能控性与能稳定性关系的时变周期系统相应结论。说明了结论是线性定常系统相应结论的自然拓展。给出了数值算例的MATLAB仿真求解过程。仿真结果验证了结论的有效性。

Abstract:

The linear time-varying periodic system is a kind of important and less investigated system which has extensive application background The basic application instances are intrduced. Two necessary conditions to judge the controllability and observability of time-varying periodic systems are obtained. The determinant condition has such a merit of not calculating the system state transition matrix that it is simple and easy to judge the controllability and observability of time-varying periodic system. The stabilizability issue of the time-varying periodic system under state feedback is considered. The parallel result of controllability and stabilizability of linear time invariant system is derived. It extends the corresponding conclusion of linear time invariant system. The MATLAB numerical example simulation is given. Simulation results validate that the determinant conditions are effective.

张雪峰，张庆灵. 线性时变周期系统的能控性与能稳定性问题[J]. Journal of Systems Engineering and Electronics, 2010, 32(4): 812-815.

ZHANG Xue-feng, ZHANG Qing-ling. Problem on controllability and stabilizability of linear time-varying periodic system[J]. Journal of Systems Engineering and Electronics, 2010, 32(4): 812-815.