Robust D-Stability Test of LTI General Fractional Order Control Systems  

作　　者：Reza Mohsenipour Xinzhi Liu 

机构地区：[1]Department of Aerospace Engineering,Sharif University of Technology,Tehran 1458889694,Iran [2]Department of Applied Mathematics,University of Waterloo,Ontario N2L 3G1,Canada

出　　处：《IEEE/CAA Journal of Automatica Sinica》2020年第3期853-864,共12页自动化学报（英文版）

摘　　要：This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.

关 键 词：FRACTIONAL order control SYSTEM LTI SYSTEM ROBUST D-STABILITY VALUE SET 

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]