Stability in Neutral Equations

Abstract

Coupled systems of differential-difference and ordinary difference equations occur in various applications including the theory of transmission lines (1) and gas dynamics (2). Stability of linear systems has been discussed by Brayton (1) using Laplace transform and the problem of absolute stability by Rasvan (12) using the frequency domain method of Popov. In this paper, the same problems are discussed by the following method. By differentiating the difference equation, one obtains a system of neutral differential-difference equations. The desired solutions of the original problem are obtained by restricting the initial data to lie on certain manifolds in the space of all initial data. In this way, this class of problems can be treated in a natural manner using the known methods of neutral equations. Generalizations to arbitrary functional differential equations is also immediate when this approach is employed.

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Document Details

Document Type
Technical Report
Publication Date
Feb 04, 1976
Accession Number
ADA027855

Entities

People

  • Jack K. Hale
  • Pedro Martinez-amores

Organizations

  • Brown University

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Difference Equations
  • Differential Equations
  • Equations
  • Frequency Domain
  • Gas Dynamics
  • Information Processing
  • Information Systems
  • Integrals
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Rhode Island
  • Transmission Lines
  • United States
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.

Technology Areas

  • Space