Feedback and Impulse Behavior of Differential-Algebraic Equations

A controlled linear system of differential-algebraic equations with infinitely differentiable coefficients is considered. An arbitrarily high unsolvability index and a variable rank of matrix coefficients are allowed. Sufficient existence conditions are obtained and methods are proposed for finding a feedback control such that the solution of a closed system exists in the class of generalized function (distribution)s of Sobolev–Schwartz type and does not contain singular terms. This control is constructed as a linear combination of the components of the system's state and its derivatives.