计算包含所有Hurwitz区间多项式根的Kharitonov型扇区的算法
Algorithm to Compute a Kharitonov-Type Sector Containing All Roots of Hurwitz Interval Polynomials
AI总结：
本文提出一种算法，用于确定复区间Hurwitz多项式所有根是否位于复平面上的指定角扇区内，通过评估有限的额外Kharitonov多项式并利用对称性提高效率。
摘要：
本文提出了一种用于复区间Hurwitz多项式的Kharitonov型算法，用于确定给定区间多项式的所有根是否位于复平面上指定的角扇区内。该方法需要评估一组有限的额外Kharitonov多项式。对于复系数不确定性，最多需要十六个这样的多项式，而在实系数情况下最多需要八个。引入了一种基于二分法的细化过程来计算一个包含所有根角度的扇区。该算法逐步收紧扇区边界，可以达到任意小的精度。在实系数情况下，构造的对称性允许直接从复情况推导出实Kharitonov结果。数值实验表明，最小包含扇区与由顶点多项式确定的扇区或可能由其中一部分确定。
英文摘要：
This paper presents a Kharitonov-type algorithm for complex interval Hurwitz polynomials that determines whether all roots of a given interval polynomial lie within a prescribed angular sector of the complex plane. The method requires evaluating a finite set of additional Kharitonov polynomials. For complex coefficient uncertainty, up to sixteen such polynomials are sufficient, while in the real-coefficient case up to eight are needed. A bisection-based refinement procedure is introduced to compute a containing sector that encloses the angles of all roots. The algorithm progressively tightens the sector bounds and can achieve arbitrarily small accuracy. In the real-coefficient case, the symmetry of the construction allows the real Kharitonov result to be derived directly from the complex case. Numerical experiments suggest that the minimal containing sector coincides with the sector determined by the vertex polynomials, or possibly by a subset of them.
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