Disturbance rejection of left-invertible systems

A new approach is presented for the study of the disturbance rejection of left-invertible systems via 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 existence of a solution to the disturbance rejection problem are established in a form of simple algebraic criteria (thus reducing the computational effort over known results) and the general analytical expressions of all solutions of the controller matrices are derived. These solutions are parameterized only by an arbitrary matrix.