REPRESENTATION AND REALIZATION OF TIME-VARIABLE LINEAR SYSTEMS

Abstract

This research emphasizes those system properties and concepts that can be characterized without solving time-variable differential equations. Criteria are developed for determining the degree of controllability and observability of a time-variable system. These criteria are based on the rank of the controllability and observability matrices, newly defined quantities formed from the system coefficient matrices and a finite number of their derivatives. Based on the theory of equivalent systems and the criteria for controllability and observability, a new approach to the synthesis of nonstationary impulse response matrices is developed. This method of synthesis, which does not require an a priori assumption of separability, provides a systematic procedure for realizing a wide class of impulse responses. By relating the concepts of controllability and unilateral transmission, the existence of a class of unilateral networks composed solely of two-terminal RC (time-variable) components is demonstrated. A stable example of such a network is presented and possible applications discussed.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1966
Accession Number
AD0488395

Entities

People

  • Leonard M. Silverman

Organizations

  • Columbia University

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Amplifiers
  • Analog Computers
  • Analytic Functions
  • Circuit Analysis
  • Computers
  • Control Systems
  • Differential Equations
  • Digital Computers
  • Electrical Engineering
  • Electrical Networks
  • Engineering
  • Equations
  • Linear Filtering
  • New York
  • Parametric Amplifiers
  • Scalar Functions
  • United States

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.