STABILITY THEORY AND ADJOINT OPERATORS FOR LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS,
RAND CORP SANTA MONICA CALIF
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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 dxdt Atx, x0 c, where t is a real variable, x is a column vector with n rows, and At is an n- by -n matrix, and a perturbed system 2 dxdt At Bt 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.