Impulse Transfer Matrix of a Time-Varying System of Differential-Algebraic Equations

Abstract

A range of issues related to the impulse transfer matrix of a system of linear differential-algebraic equations is considered. For systems with infinitely differentiable coefficients, it is shown that this matrix can be represented as the sum of the impulse transfer matrices of its differential and algebraic subsystems. A form of a nondegenerate change of variables is found, which does not affect the form of the impulse transfer matrix. It is proposed to search for realizations of this matrix in the class of differential-algebraic equations of index 1 with separated differential and algebraic components. Necessary and sufficient conditions for the realizability of an impulse transfer matrix in the class of algebraic systems are obtained. The problem of construction methods and the dimension of minimal realizations of such a matrix is discussed under various assumptions.