Abstract: The problem of robust D-stability analysis with respect to an LTI SISO feedback system is studied. First, the geometric properties of the sum of the segments in the complex plane are proved, Based on which, the robust problem is interpreted as a special point location problem of computing geometry. Therefore, some necessary and sufficient conditions for the stability of the perturbed systems subject to the robust performance are proposed. Then, several efficient algorithms are presented using computational geometric techniques.

Key words: D-stability, stability radius, geometric approach

摘要： 研究了线性时不变单输入单输出反馈系统的鲁棒D-稳定性问题。证明了在复平面上多个线段和的几何性质。在此基础上，将鲁棒问题转化为计算几何中的点定位问题。从而得到扰动系统在满足一定稳定指标约束条件下，系统稳定的充分必要条件。利用计算几何的方法，给出了相应的算法。

关键词: 鲁棒D-稳定性, 稳定半径, 几何算法