Tallinn University of Technology, Department of Computer Systems, Estonia.
ISA Trans. 2022 Oct;129(Pt B):140-151. doi: 10.1016/j.isatra.2022.02.014. Epub 2022 Feb 15.
This paper studies the problem of robust stabilization of interval fractional-order plants with complex uncertain parameters by using fractional-order controllers. An interval fractional-order plant with complex uncertain parameters means that the coefficients of the numerator and denominator of the plant are all uncertain and may be complex numbers and lie in specified intervals. At first, by using a graphical approach, necessary and sufficient conditions are presented for the stabilization of the fractional-order plant containing complex coefficients. Then, by using some interesting geometric features of convex polygons, a robust stability checking function is presented for the stabilization. Also, an upper frequency bound is introduced to reduce the computational burden. Finally, six examples are provided to illustrate the results.
本文研究了利用分数阶控制器对具有复杂不确定参数的区间分数阶系统进行鲁棒稳定化的问题。具有复杂不确定参数的区间分数阶系统是指，系统的分子和分母系数均为不确定的，并且可能是复数，且位于指定区间内。首先，通过图形方法，给出了包含复数系数的分数阶系统稳定的充分必要条件。然后，利用凸多边形的一些有趣的几何特征，给出了一个用于稳定化的鲁棒稳定性检验函数。此外，引入了一个上限频率来降低计算负担。最后，提供了六个示例来说明结果。
