算子值加权模式在Banach空间的实现理论

REALIZATION THEORY IN BANACH SMCE FOR OPERATOR-VALUED WEIGHTING PATTERNS

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．

This paper deals with linear continuous-time systems that can be realized on Banach spaces. The input, output and state spaces here are all infinite-dimensional Banach spaces. We prove that a weighting pattern has a Banach space realization if and only if it is strongly continuous and of exponential order. An existence theorem of the Banach space realizations when the state operators are the infinitesimal generators of analytic semigroups is obtained. All the theorems are given in the time domain.