一种线性分数阶系统稳定性的频域判别准则

A Stability Criterion for Linear Fractional Order Systems in Frequency Domain

在分析了分数阶系统稳定性与传递函数分母相角增量的关系的基础上,提出了一种线性分数阶系统的频域稳定性判别定理.定义了关于分数阶系统分母各项系数的两个函数,通过分析这两个函数正实数解的大小关系以及解的数目与分母最高阶数的关系,给出了分数阶系统稳定所需满足的条件.将用于在频域上对整数阶系统稳定性判别的Hermite-Biehler定理推广到对分数阶系统稳定性的判定.最后,通过对两个数值算例的分析,说明了提出的稳定性判别准则的正确性.

A stability theorem for linear fractional order systems is proposed by analyzing the relationship between the phase angle increment of the denominator of the transfer function and the stability in the frequency domain. Two functions about the denominator coefficients are defined, the stability conditions are presented by analyzing the relationship of the positive real solutions of these two functions and the relationship between the number of solutions and the highest order of the denominator. This stability theorem generalizes the Hermite-Biehler theorem for integer order linear systems and extend it to fractional order systems in the frequency domain. Finally, the results of two numerical examples are analyzed to illustrate the validity of the proposed stability theorem.