摘要
本文基于LMI方法研究线性时变周期分数阶(0<α<1)系统的鲁棒控制及稳定性分析问题。为了避开求解复杂系统的状态转移矩阵,文中借鉴解决线性定常系统鲁棒控制问题的思想以及分数阶系统稳定性理论,将周期问题转变为讨论范数有界问题;针对LTVP分数阶系统设计无记忆反馈控制器,应用线性矩阵不等式(LMI)的方法 ,给出使闭环系统渐进稳定的充要条件,并用仿真算例验证所提出方法的有效性。
This paper concerns with the robust control and stability analysis of the linear time-varying periodic fractional-order systems with the fractional commensurate orderα （0〈α〈1）. By using the thought of solving robust control of the linear time invariant systems and the stability theory of fractional-order differential system, the periodic problem is converted into a kind of norm bounded problems. The calculation of the state transition matrix of LTVP systems is avoided. The linear matrix inequalities （LMIs） based memoryless state controllers of stabilization of LTVP fractional-order systems are designed and two suffcient and necessary conditions for robust asymptotical stability of the closed-loop control systems are presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed methods.
作者
张会珍
刘宝江
任伟建
邵克勇
ZHANG Hui-zhen;LIU Bao-jiang;REN Wei-jian;SHAO Ke-yong(School of Electrical Engineering ＆ Information Northeast Petroleum University,Daqing 163318 China)
出处
《自动化技术与应用》
2018年第11期6-10,共5页
Techniques of Automation and Applications
基金
黑龙江省教育厅科学技术研究项目(编号12541090)
国家自然科学基金项目(编号51404073)
关键词
周期系统
稳定性
线性矩阵不等式
鲁棒控制
分数阶系统
periodic systems
stability
linear matrix inequalities
robust control
fractional-order system
