内算子值函数的可实现性(英文)

Realization of Inner Operator-valued Functions

本文讨论内算子值函数的态空间实现问题 .证明了任何一个内算子值函数都具有正合的无限时间可控和正合的可观测的适定的系统实现 .在此基础上 ,我们还得到相关C0 半群为指数稳定的或成为一个群的充分必要条件 ,从而推广了 [3]中的相应结果 .

In this paper, we investigate the state space realization of inner operator valued functions. We show that any inner operator valued function has an exact infinite time controllable and exact observable well posed realization. We also derive some necessary and sufficient conditions on basis of the inner operator valued function such that the associated C 0 semigroup is exponentially stable or a group, generalizing the corresponding results in [3] to the operator valued function case.