STABILITY THEORY AND ADJOINT OPERATORS FOR LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS,

Abstract

This paper extends to linear differential-difference equations a number of results familiar in the stability theory of ordinary linear differential equations. In this theory, one considers a system of equations of the form (1) dx/dt = A(t)x, x(0) = c, where t is a real variable, x is a column vector with n rows, and A(t) is an n- by -n matrix, and a perturbed system (2) dx/dt = (A(t) + B(t) )x. In general terms, the stability problem is to determine conditions on the matrix B sufficient to ensure that some property of all solutions of (1)- such as boundedness or order of growth - will also be a property of all solutions of (2).

Document Details

Document Type
Technical Report
Publication Date
Feb 14, 1958
Accession Number
AD0606842

Entities

People

  • K. L. Cooke
  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Difference Equations
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Nonlinear Differential Equations
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra