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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。
The problem of robust D stability for linearly invariant single-input and single-output feedback systems is investigated. The geometrical properties of multiple segments and their complexities on the complex plane are proved. On this basis, the robust problem is transformed into the problem of point location in computational geometry. The sufficient and necessary conditions for the stability of the system under perturbation are obtained. Using the method of calculating geometry, the corresponding algorithm is given.