Realization Theory in Hilbert Space

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1985
Accession Number
ADA158172

Entities

People

  • Dietmar Salamon

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Classification
  • Contracts
  • Control Systems
  • Differential Equations
  • Equations
  • Hilbert Space
  • Identities
  • Inequalities
  • Invariance
  • Linear Systems
  • Mathematics
  • New York
  • Partial Differential Equations
  • Space Systems
  • United States

Fields of Study

  • Mathematics

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  • Space