Minimal Passive Realizations of Generalized Schur Functions in Pontryagin Spaces
Minimal Passive Realizations of Generalized Schur Functions in Pontryagin Spaces
复制标题
Pontryagin 空间中广义 Schur 函数的最小无源实现
DOI：
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发表时间：
2019
影响因子：
0.8
通讯作者：
Lassi Lilleberg
中科院分区：
文献类型：
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作者：
Lassi Lilleberg
研究了庞特里亚金空间中的无源离散时间系统。在这种情况下，被动系统的传递函数或压缩算子类的特征函数是广义Schur函数。证明了最优和∗文档类[12pt]{Minimum}usepackage{amsath}usepackage{wa ysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{matrsfs}usepackage{upgreek}setlong{oddsidemargin}{-69pt}例如{Document}$$*$$end{Document}-广义舒尔函数的最优最小实现.在此基础上，给出了广义Schur函数的一种新定义。将D.Z.Arov和M.A.Nudelman在同一Schur函数的所有极小无源实现酉性相似时的一个判据推广到广义Schur函数类。这里使用的方法是新的；它完全依赖于被动系统理论。
Passive discrete-time systems in Pontryagin space setting are investigated. In this case the transfer functions of passive systems, or characteristic functions of contractive operator colligations, are generalized Schur functions. The existence of optimal and ∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$^*$$end{document}-optimal minimal realizations for generalized Schur functions are proved. By using those realizations, a new definition, which covers the case of generalized Schur functions, is given for defects functions. A criterion due to D.Z. Arov and M.A. Nudelman, when all minimal passive realizations of the same Schur function are unitarily similar, is generalized to the class of generalized Schur functions. The approach used here is new; it relies completely on the theory of passive systems.