A new approach is presented for the study of the disturbance rejection of left-invertible generalized state space systems via pure proportional state feedback, reducing the problem to that of solving a linear algebraic system of equations. On the basis of this system of equations, the necessary and sufficient conditions for the problem to have a solution are established in a form of simple algebraic criteria (thus reducing the computational effort over known results), and the general analytical expressions of the controller matrices are derived. The structural properties of the closed-loop system (feedback invariant poles, disturbance rejection with simultaneous elimination of the infinite poles) are studied.