Minimal realizations of MIMO systems

Abstract

Minimal realization permits to accurately represent a system in state space form with a minimal order. This research work presents some important results in system modelling concerning minimal realization and model reduction. The first result is about minimal realizations of MIMO LTI systems. The resulting form is in a canonical form. The second result is about model reduction based on matrix polynomials. These two presented algorithms are specifically designed for MIMO systems. Finally, important results for minimal realization of Port Hamiltonian systems are presented. These results are unprecedented and constitute an important step in Port Hamiltonian systems modelling