A Liapunov Functional for a Matrix Difference-Differential Equation,

Abstract

A quadratic positive definite functional that yields necessary and sufficient conditions for the asymptotic stability of the solutions of the matrix difference-differential equation dx(t)/dt=Ax(t) + Bx(t-tau) is constructed and its structure analyzed. This functional, a Liapunov functional, provides the best possible estimate for the rates of growth or decay of the solutions of this equation. The functional obtained, and its method of construction, are natural generalizations of the same problem for ordinary differential equations, and this relationship is emphasized. An example illustrates the applicability of the results obtained. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 21, 1977
Accession Number
ADA042627

Entities

People

  • Ettore Ferrari Infante
  • W. B. Castelan

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • C4I
  • Counter IED

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computations
  • Construction
  • Difference Equations
  • Differential Equations
  • Equations
  • Integrals
  • Linear Systems
  • Mathematics
  • Notation
  • Real Numbers
  • Scalar Functions
  • Square Roots
  • Two Dimensional
  • United States
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis