Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems
Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems
复制标题
具有多次演化的散射系统和多维输入/状态/输出系统
DOI：
10.1007/s00020-005-1351-y
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发表时间：
2005
影响因子：
0.8
通讯作者：
V. Vinnikov
中科院分区：
文献类型：
--
作者：
J. Ball;C. Sadosky;V. Vinnikov
摘要：一维线性（平稳的，因果的）输入/状态/输出系统和具有一个演化算子的散射系统之间的一一对应关系，其中散射系统的散射函数与线性系统的传递函数一致，已经很好地理解，并且在H∞控制理论中有重要的应用。在这里，我们认为这种对应关系中的d维设置中的转移和散射函数的定义上的polydisk。与一维情况不同，多维状态空间实现和相应的多演化散射系统不一定是等价的，并且d = 2和d > 2的情况有很大不同。作为分析的推论，得到了交换压缩算子对的Andô膨胀定理的一个新证明和双圆盘上矩阵值内函数的一个新的状态空间实现定理.
Abstract.The one-to-one correspondence between one-dimensional linear (stationary, causal) input/state/output systems and scattering systems with one evolution operator, in which the scattering function of the scattering system coincides with the transfer function of the linear system, is well understood, and has significant applications in H∞ control theory. Here we consider this correspondence in the d-dimensional setting in which the transfer and scattering functions are defined on the polydisk. Unlike in the onedimensional case, the multidimensional state space realizations and the corresponding multi-evolution scattering systems are not necessarily equivalent, and the cases d = 2 and d > 2 differ substantially. A new proof of Andô’s dilation theorem for a pair of commuting contraction operators and a new statespace realization theorem for a matrix-valued inner function on the bidisk are obtained as corollaries of the analysis.