Realization Theory in Hilbert Space
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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. Additional keywords Linear control systems Frechet space.
- Theoretical Mathematics