Tan Nusret, Ozgüven O Faruk, Ozyetkin M Mine
Inonu University, Engineering Faculty, Department of Electrical and Electronics Engineering, 44280, Malatya, Turkey.
ISA Trans. 2009 Apr;48(2):166-72. doi: 10.1016/j.isatra.2009.01.002. Epub 2009 Feb 3.
The paper deals with the robust stability analysis of a Fractional Order Interval Polynomial (FOIP) family. Some new results are presented for testing the Bounded Input Bounded Output (BIBO) stability of dynamical control systems whose characteristic polynomials are fractional order polynomials with interval uncertainty structure. It is shown that the Kharitonov theorem is not applicable for this type of polynomial. A procedure is given for computation of the value set of FOIP. Based on the value set, an algorithm is presented for testing the stability of FOIP. The results presented in the paper are useful for the analysis and design of Fractional Order Interval Control Systems (FOICS). Examples are given to show how the proposed method can be used to assess the effects of parametric variations on the stability in feedback loops with fractional order interval transfer functions.
本文研究了分数阶区间多项式（FOIP）族的鲁棒稳定性分析。针对特征多项式为具有区间不确定性结构的分数阶多项式的动态控制系统，给出了一些用于测试有界输入有界输出（BIBO）稳定性的新结果。结果表明，卡里托诺夫定理不适用于此类多项式。给出了一种计算FOIP值集的方法。基于该值集，提出了一种测试FOIP稳定性的算法。本文给出的结果对于分数阶区间控制系统（FOICS）的分析和设计具有重要意义。通过实例展示了所提方法如何用于评估具有分数阶区间传递函数的反馈回路中参数变化对稳定性的影响。
