Associating matrix pencils to generalized linear multivariable systems

We consider quadruples of matrices (E,A,B,C) representing generalized linear multivariable systems with E, A square matrices and B, C rectangular matrices. We characterize equivalent quadruples, by associating matrix pencils to them, with respect to the equivalence relation corresponding to standard transformations: basis changes (for the state, control and output spaces), state feedback, derivative feedback and output injection. Equivalent quadruples are those whose associated matrix pencils are “simultaneously equivalent”.