Some new rearrangement inequalities having application in stability analysis
Some new rearrangement inequalities having application in stability analysis
复制标题
一些新的重排不等式在稳定性分析中的应用
DOI：
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发表时间：
1968
期刊：
影响因子：
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通讯作者：
R. Brockett
中科院分区：
文献类型：
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作者：
J. Willems;R. Brockett
Sylvester检验是建立二次型正性的基本工具，但对于非二次型，正性的充分必要条件通常是未知的。这里给出了summin{k，l=1}max{n} x_{k}m_kl}f（x_{1}）类型为正的几个简单的充要条件。这些结果是通过将Hardy， Littlewood和Polya的经典结果与双随机矩阵的Birkhoff表征相结合而得出的。结果应用于控制非线性反馈回路的差分方程。在这种情况下，它们为稳定产生了新的和相当普遍的条件。
The Sylvester test for establishing the positivity of quadratic forms is a basic tool For nonquadratic forms, however, necessary and sufficient conditions for positivity are generally not known. Given here are some simple necessary and suffcient conditions for forms of the type summin{k,l=1}max{n} x_{k}m_kl}f(x_{1}) to be positive. These results are derived by combining a classic result of Hardy, Littlewood, and Polya with the Birkhoff characterization of doubly stochastic matrices. The results are applied to the difference equations governing a nonlinear feedback loop. In this setting they yield new and quite general conditions for stability.