多项式族稳定性判定问题的多项式算法

A POLYNOMIAL-TIME ALGORITHM FOR THE STABILITY-ROBUSTNESS CHECKING PROBLEM OF POLYNOMIAL-FAMILIES

利用除零原则，多项式族稳定性的判定问题（系数仿射依赖于参数的情形）可以化为单参数秩２简单二次规划问题。本文用二次规划的理论、Ｋｕｈｎ－Ｔｕｃｋｅｒ条件，提出了此问题的一个多项式时间算法。可以看到许多重要的结果，如棱边定理和强Ｋｈａｒｉｔｏｎｏｖ定理仅是此算法的一个特例。作为简单应用，介绍了区间多项式族ｓｃｈｕｒ问题的一个具体算例。

Consider the stability-robustness of a polynomial-family (assuming that the coefficients are affine functions of the parameters). This problem can be converted to an one-parameter simple quadratic programming (rank 2) by the zero-excluding principle. Using the theory of simple quadratic programming, the Khun-Tucker conditions and the method of perturbation analysis we derive a polynomial-time algorithm and solve the problem of computing complexity. Most of the availabe results in the literature, such as the Edge Theorem and the Extended Kharitonov's Theorem arespecial cases of the algorithm developed in this paper.