Analytic determination of the null space of singular pencil of matrices

For eigenstructure assignment in linear control systems, it is necessary to select the eigenvectors or reciprocal eigenvectors of the closed-loop plant matrix. These vectors belong to two well-defined families of vector spaces parametrized by the plant, input, and output matrices. In this paper, a simple method for the analytic determination of these vector spaces is presented based on the controllable canonical form of the system.