频率域α-阶分数阶系统的稳定性判据:1 < α < 2情况

Zhe Gao, X. Liao, Bo Shan, Hong Huang
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引用次数: 1

摘要

给出了相应阶数α满足1 <的线性分数阶系统的稳定性判据;α<;2. 研究了线性分数阶系统中特征函数的角度增量问题,给出了系统在频域上关于角度增量的稳定性条件。在此条件下,根据两个方程关于特征函数系数和最高阶系数的正实解的排列,给出了验证线性分数阶系统稳定性的稳定性判据。最后通过数值算例验证了所提稳定性判据的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A stability criterion for fractional-order systems with α-order in frequency domain: The 1 < α < 2 case
This paper proposes a stability criterion for linear fractional-order systems with the commensurate order α satisfying 1 <; α <; 2. The angle increment of the characteristic function in a linear fractional-order system is investigated, and the stability condition with respect to the angle increment is presented in the frequency domain. By this condition, we present a stability criterion to verify the stability of a linear fractional-order system according to the arrangement of the positive real solutions of two equations with respect to the coefficients of the characteristic function and the highest order. Finally, a numerical example is given to demonstrate the effectiveness of the proposed stability criterion.
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