Riccati equations for abnormal time scale quadratic functionals
Riccati equations for abnormal time scale quadratic functionals
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异常时间尺度二次泛函的 Riccati 方程
DOI：
10.1016/j.jde.2007.10.012
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发表时间：
2008
影响因子：
2.4
通讯作者：
V. Zeidan
中科院分区：
文献类型：
--
作者：
R. Hilscher;V. Zeidan
本文主要研究反常时标辛系统（S）的新的Riccati型条件。这些条件提供了与这样一个系统相关的二次泛函的非负性（有和没有一定的“图像条件”）和正性的表征。这些条件的新奇性依赖于（S）的自然联合基（Xa，Ua），其中Xa（t）不一定可逆，因此系统（S）可能是异常的。这些结果是新的，即使在连续时间的特殊情况下，因为其中一些在离散时间设置。
This paper focuses on developing new Riccati type conditions for an abnormal time scale symplectic system (S). These conditions provide characterizations of the nonnegativity (with and without a certain “image condition”) and positivity of the quadratic functionals associated with such a system. The novelty of these conditions rely on the natural conjoined basis (Xa,Ua) of (S) in which Xa(t) is not necessarily invertible, and thus the system (S) could be abnormal. These results are new even in the special case of continuous time, as are some of them in the discrete time setting.