Realization of Continuous-Time Linear Dynamical Systems: Rigorous Theory in the Style of Schwartz,

Abstract

The paper gives a rigorous definition of the input/output map of a linear constant dynamical system using generalized functions in the style of Schwartz. It is proved, using only natural constructions, that the minimal realization of such a system is governed by linear differential equations with constant coefficients (in the sense of Kalman). This is the first time such a result has been obtained; previous work required ad-hoc assumptions or lacked rigor. As a result of the theory developed in this paper, precise conditions are now known for the applicability of module theoretic-methods to the theory of continuous-time linear systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1971
Accession Number
AD0734281

Entities

People

  • M. L. J. Hautus
  • R. E. Kalman

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Construction
  • Cooperation
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Netherlands
  • Nonlinear Differential Equations
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.