On the Computation of Minimal Polynomial Bases

—The problem of determination of a minimal polynomial basis of a rational vector space is the starting point of many control analysis, synthesis and design techniques. In this paper, we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s). The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants, in order to compute ef ciently row polynomial vectors that form a minimal polynomial basis of the left kernel of the given polynomial matrix. One of the advantages of the algorithm is that it can be implemented using only orthogonal transformations of constant matrices and the result is a minimal basis with orthonormal coef cients.