Global reduction to the Kronecker canonical form of a Cr-family of time-invariant linear systems Original Research Article

We present an approach to the Kronecker equivalence of quadruples of matrices (A, B,C, D) based on a natural equivalence relation between pairs of linear mappings. We apply this approach to smooth families of quadruples of constant Kronecker type, obtaining smooth families of transformation matrices that pointwise reduce each quadruple to its Kronecker canonical form.