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 \(^*\)-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.

中文翻译：

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Pontryagin空间中广义Schur函数的最小无源实现

研究了蓬特里亚金空间设置中的无源离散时间系统。在这种情况下，无源系统的传递函数或契约算子组合的特征函数是广义Schur函数。证明了广义Schur函数的最优和\（^ * \）最优最小实现的存在。通过使用这些实现，为缺陷函数给出了涵盖广义Schur函数情况的新定义。当同一Schur函数的所有最小无源实现都统一相似时，由DZ Arov和MA Nudelman提出的准则将推广到广义Schur函数的类。这里使用的方法是新的。它完全依赖于无源系统的理论。