This article deals with the problem of robust fractional-order fixed-structure controller design for commensurate and non-commensurate fractional-order interval systems using fractional Kharitonov theorem. The contribution of this study is to develop a simple control methodology to stabilize the fractional-order Kharitonov-defined vortex polynomials. Using the idea of robust stability testing function and extending it to the systems under study, the straightforward graphical and systematic procedures are proposed to investigate the robust stability of the system by searching for a non-conservative fractional-order Kharitonov region in the controller parameters plane. This region can establish all the fractional-order controllers that make the uncertain fractional-order systems stable. The relation between the fractional-order Kharitonov region and the parameters of the stabilizing controller is also found. Finally, comparison results with three relevant works are given to illustrate the feasibility of the proposed method.

本文讨论了分数阶Kharitonov定理针对相称和非相称分数阶区间系统的鲁棒分数阶固定结构控制器设计的问题。这项研究的目的是开发一种简单的控制方法来稳定分数阶Kharitonov定义的涡旋多项式。利用鲁棒稳定性测试功能的思想并将其扩展到正在研究的系统中，提出了简单的图形化和系统性程序，以通过在控制器参数平面中搜索非保守分数阶Kharitonov区域来研究系统的鲁棒稳定性。 。该区域可以建立所有使不确定分数阶系统稳定的分数阶控制器。还发现了分数阶Kharitonov区域与稳定控制器参数之间的关系。最后，通过与三项相关工作的比较结果，说明了该方法的可行性。