Realization Theory in Hilbert Space

摘要

This paper studies the state space representation of time invariant causal, linear input-output operators in continuous time. A realization theorem in the Hilbert space context is established in full generality using unbounded input and output operators. The first step is to construct an abstract state space representation with a prescribed input-output behavior. The second step is to transform this abstract system into a differential equation. The uniqueness problem is discussed in some detail as well as the relation to existing results in realization theory. (Author)