线性系统同时极点配置的代数几何方法

Algebraic geometric method of simultaneous pole assignment of linear systems

利用代数几何方法,研究两个线性系统状态反馈和输出反馈同时极点配置问题。通过讨论代数几何中的有理映射是否为到上的,来判别线性系统的特征多项式的系数可否几乎任意配置,从而推导出两个线性系统状态反馈和输出反馈同时极点配置的充分条件。将此结论应用到同时镇定问题上,得到了两个线性系统同时镇定的充分条件,并证明了如果两个线性系统存在复反馈同时配置极点,则一定存在实反馈同时配置极点。

The problem of simultaneous pole assignment of two linear systems via state feedback and output feedback is investigated by means of the algebraic geometric method According to the theorem in algebraic geometry that if the rational mapping is onto, it shows that coefficients of the characteristic polynomial of linear systems can be almost assigned arbitrarily. Sufficient conditions for simultaneous poles assignment of two linear systems via state feedback and output feedback are derived, respectively. Applied this result to the problem of simultaneous stabilization, sufficient conditions for simultaneous stabilization of two linear systems via state feedback and output feedback are derived, respectively. In addition, it shows that if there exists a complex feedback matrix to simultaneously assign poles in two linear systems, then there is a real feedback matrix to simultaneously assign poles.