Akbari Moornani Kamran, Haeri Mohammad
Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran.
ISA Trans. 2009 Oct;48(4):484-90. doi: 10.1016/j.isatra.2009.04.006. Epub 2009 May 24.
In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results obtained by the lemma and theorems presented in the paper.
本文分析了一大类具有实参数不确定性的线性时不变分数阶系统族的鲁棒有界输入有界输出稳定性。传递函数包含拉普拉斯变量(s)的分数幂多项式，可能还与(s)的分数幂指数相结合。利用值集的概念和零排除条件定理的推广，给出了一个用于检验这些系统族鲁棒有界输入有界输出稳定性的定理。还提供了绘制值集的上截止频率。最后，给出两个数值例子来说明本文引理和定理所得到的结果。
