<p>We consider differential-algebraic equations with hysteresis type nonlinearity (modeled by a sweeping process). The unsolvability measure with respect to the derivatives is characterized by an integer index. It is assumed that there exists a structural form with separated differential and algebraic subsystems. This structural form is equivalent to the original system in the sense of solutions, and the operator reducing the system of differential-algebraic equations to this structural form has the left inverse operator. sufficient Such systems arise in modeling physical processes, particularly electrical circuits. Sufficient solvability and controllability conditions for the original problems are obtained.</p>