区间分数阶系统的鲁棒稳定性判别准则:0<α<1情况  

Robust Stability Criteria for Interval Fractional-order Systems:The 0 < α < 1 Case

作　　者：高哲[1,2] 廖晓钟[1,2] 

机构地区：[1]北京理工大学自动化学院,北京100081 [2]复杂系统智能控制与决策教育部重点实验室(北京理工大学),北京100081

出　　处：《自动化学报》2012年第2期175-182,共8页Acta Automatica Sinica

基　　金：国家自然科学基金(10872030)资助~~

摘　　要：针对同元阶次在0和1之间的区间分数阶系统,提出了类似Kharitonov定理的鲁棒稳定性判别准则.研究了区间分数阶系统分母的主分支函数值集不包含原点所需满足的条件.根据除零原理,给出了区间分数阶系统鲁棒稳定的顶点和棱边条件.定义了由分母函数系数构成的矩阵,通过检验矩阵是否在负实轴上存在特征值来检验棱边条件.最后,通过对两个数值算例的分析说明了这种方法的有效性.This paper presents a robust stability theorem like the Kharitonov theorem for interval fractional-order systems with commensurate order between 0 and 1. The condition that the origin is not contained in the value set of the principle branch function of denominator function in an interval fractional-order system is studied. The vertex and edge conditions for interval fractional-order systems are proposed based on the zero exclusion principle. Some matrices depending on parameters of the denominator function are defined and the edge conditions are tested by checking whether eigenvalues of each matrix lie on the negative real axis. Finally, two numerical examples are analyzed to illustrate the effectiveness of the proposed method.

关 键 词：分数阶系统 区间不确定性 鲁棒稳定性 值集 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O172[自动化与计算机技术—控制科学与工程]