Polytopes of Nonnegative Polynomials
Polytopes of Nonnegative Polynomials
复制标题
非负多项式的多面体
DOI：
10.23919/acc.1989.4790187
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
D. Siljak
中科院分区：
文献类型：
--
作者：
D. Siljak
代数，递归和有限的测试，提出了验证，如果一个凸多面体的参数空间中只包含轴或圆非负多项式。一个非凡的数值简单的测试是一个后果的事实，即在参数空间中的非负区域被证明是凸的，它足以检查只有顶点多项式的多面体。该测试适用于鲁棒性分析的绝对稳定的非线性连续和离散系统，LQ调节器的最优性，有理函数和矩阵的正实性，以及多项式矩阵的正性出现在2-D多项式的稳定性准则。
Algebraic, recursive, and finite tests are proposed to verify if a convex polytope in the parameter space contains only axis or circle nonnegative polynomials. An extraordinary numerical simplicity of the tests is a consequence of the fact that the nonnegativity regions in the parameter space are shown to be convex, and it suffices to check only the vertex polynomials of the polytope. The tests are applied to robustness analysis of absolute stability of nonlinear continuous and discrete systems, optimality of LQ regulators, positive realness of rational functions and matrices, and positivity of polynomial matrices appearing in stability criteria for 2-D polynomials.