A Liapunov Functional for a Matrix Neutral Difference-Differential Equation with one Delay,

Abstract

For the matrix neutral difference-differential equation x(dot)(t) + Ax(dot(t-tau) = Bx(t) + Cx(t-tau) a quadratic Liapunov functional is constructed which gives necessary and sufficient conditions for the asymptotic stability of the solutions of that equation. A difference equation approximation is considered of the difference-differential equation, and for this difference equation a Liapunov function is constructed from which is obtained the desired Liapunov functional by an appropriate limiting process. The Liapunov functional thus obtained gives the best possible estimate for the rates of growth or decay of the solutions of the matrix neutral difference-differential equation. The results obtained are natural generalizations of previous results obtained for a matrix retarded difference-differential equation with one delay.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1977
Accession Number
ADA049868

Entities

People

  • Ettore Ferrari Infante
  • W. B. Castelan

Organizations

  • Brown University

Tags

Communities of Interest

  • Autonomy
  • C4I

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computations
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Integrals
  • Mathematics
  • Notation
  • Numbers
  • Real Numbers
  • Square Roots
  • Theorems
  • Vector Spaces
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Fields of Study

  • Mathematics

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