一类不确定奇异分数阶系统的保成本控制
Guaranteed Cost Control for a Class of Uncertain Descriptor Fractional-order Systems
投稿时间:2019-11-19  修订日期:2019-11-19
DOI:
中文关键词: 分数阶系统  保成本控制  奇异系统  参数不确定性
英文关键词: Fractional-order system  guaranteed cost control  descriptor systems  parameter uncertainties
基金项目:
作者单位E-mail
杨占英 数学与统计学学院 yangzhanying8011@163.com 
张杰 数学与统计学学院 15527290045@163.com 
蔡明建 数学与统计学学院  
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中文摘要:
      本文研究了阶数在0到1的不确定奇异分数阶系统,并给出了保成本反馈控制的设计方法。参数的不确定性设定为时变有界,出现在状态矩阵中。首先,利用线性矩阵不等式,给出实现系统规范化的充要条件,利用此条件,将奇异系统改写为规范化系统,同时给出保成本函数;然后,直接对李雅普诺夫方程求导来得到一个系统渐进稳定的充分条件;最后,用数值仿真证明了方法的可行性。
英文摘要:
      . This paper investigates uncertain descriptor fractional-order systems with order ,the design method of guaranteed cost feedback control is derived. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in the state matrix. Firstly, we give a necessary and sufficient condition to achieve the normalization of uncertain descriptor fractional-order systems by linear matrix inequality (LMI) formulation, then, we rewrite the descriptor system as a normalized system by using the condition, meanwhile, the guaranteed cost function is given. Secondly, we directly calculate fractional-order derivatives of the Lyapunov functions to get a sufficient condition such that the normalized system could be asymptotically stable. Finally, a simple numerical example is given to demonstrate the feasibility of the proposed method.
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