Stability Theory and Adjoint Operators for Linear Differential-Difference Equations

摘要

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).