不确定分数阶奇异系统鲁棒控制及稳定性分析

Robust Control and Stability Analysis of Uncertain Descriptor Fractional Order Systems

针对不确定线性分数阶奇异系统的鲁棒稳定性问题,将连续频率分布等价模型引入分数阶奇异系统中,应用间接李亚普诺夫方法,设计了一个PD(Proportional-Derivative)控制器,将奇异系统正常化,给出了阶次在0<α<1范围内分数阶奇异系统全新的鲁棒渐近稳定的充分条件。利用Matlab的LMI(Linear Matrix Inequalities)工具箱及矩阵的奇异值分解(SVD:Singular Value Decomposition)求解控制器的增益,用仿真算例及数据验证该方法的有效性。

In order to solve the problem of the stability analysis of the linear descriptor fractional-order systems, the continuous frequency distributed equivalent model and the indirect Lyapunov approach are applied in the research of the linear descriptor fractional-order systems, an PD （Proportional-Derivative） controller is proposed to normalize the descriptor fractional order system. A novel sufficient condition for asymptotic stability of the descriptor fractional-order system with the order α （0 〈 α 〈 1 ） is presented. LMI （ Linear Matrix Inequalities） techniques and matrix＇s SVD （ Singular Value Decomposition ） are used to obtain the results. A numerical example is provided to demonstrate the effectiveness of the proposed methods.