An alternative system of structural invariants of quadruples of matrices Original Research Article

The equivalence relation between time-invariant linear dynamical systems deduced from the action of the group consisting of all basis changes, state feedback and output injection transformations is considered. An alternative complete system of structural invariants is presented. Discrete invariants in this system are the ranks of suitable matrices, generalizing the numerical invariants obtained for pairs of matrices under block-similarity. The continuous invariants are characterized in terms of the rank of a matrix.