Feedback Elimination of Impulse Terms from the Solutions of Differential-Algebraic Equations

We consider a controlled linear system of differential-algebraic equations with infinitely differentiable coefficients that is allowed to have an arbitrarily high unsolvability index. It is assumed that the matrix multiplying the derivative of the desired vector function has a constant rank. We prove a theorem on the existence of a solution in the class of Sobolev-Schwartz type generalized functions and derive conditions for the existence of a feedback control such that the general solution of the closed-loop system does not contain singular terms. The relation of these conditions to impulse controllability is shown.