On the definiteness of quadratic functionals
On the definiteness of quadratic functionals
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关于二次函数的定性
DOI：
10.1007/bf02505993
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发表时间：
1999
影响因子：
1
通讯作者：
R. Schätzle
中科院分区：
文献类型：
--
作者：
W. Kratz;Dirk Liebscher;R. Schätzle
本文给出了时变线性系统强能观性（或具有未知输入的能观性）的各种刻画
$$\dot x = Ax + Bu，y = C_0 x$$
假设矩阵A、B和C 0足够平滑，则具有状态x、控制u和输出y。我们表明，强可观性是等价于一个相应的二次泛函的确定性，特别是相关的Riccati矩阵微分方程的解的一定的渐近行为。证明的主要工具是Ehrling引理的应用和通过矩阵的秩条件对强可观测性的表征，所述矩阵由矩阵A、B和C 0的导数建立。
AbstractIn this paper we derive various characterizations of strong observability (or observability with unknown inputs) of time-dependent linear systems
$$\dot x = Ax + Bu,y = C_0 x$$
with state x, control u, and output y, provided that the matrices A, B, and C0 are smooth enough. We show that strong observability is equivalent to the definiteness of a corresponding quadratic functional, and particularly to a certain asymptotic behaviour of solutions of associated Riccati matrix differential equations. The main tools for the proofs are an application of Ehrling's lemma and a characterization of strong observability via a rank condition on matrices, which are built up from derivatives of the matrices A, B, and C0.