Duality for Linear Systems: External and State Space Characterization of the Adjoint System
Duality for Linear Systems: External and State Space Characterization of the Adjoint System
复制标题
线性系统的对偶性：伴随系统的外部和状态空间表征
DOI：
10.1007/978-1-4612-3214-8_35
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发表时间：
1990
影响因子：
3.2
通讯作者：
A. J. Schaft
中科院分区：
文献类型：
--
作者：
A. J. Schaft
在给出以状态空间形式给出的线性系统伴随系统的内在定义之后，我们用系统的外部行为来表征伴随系统。相反，我们展示了这种外部表征如何允许人们通过构造从伴随系统的抽象定义的最小状态空间到系统本身的最小状态空间的对偶的同构来恢复状态空间的定义。给出了如何从Bezoutian矩阵的修正形式得到这种同构的坐标表达式。
After providing an intrinsic definition of the adjoint system of a linear system given in state space form, we characterize the adjoint system in terms of the system’s external behavior. Conversely we show how this external characterization allows one to recover the state space definition by constructing an isomorphism from the abstractly defined minimal state space of the adjoint system to the dual of the minimal state space of the system itself. It is shown how a coordinate expression of this isomorphism can be obtained from a modified form of the Bezoutian matrix.