Minimal periodic realizations of transfer matrices

Periodic controllers designed based on the so-called lifting technique are usually represented by transfer matrices. Real operations require that the controllers be implemented as periodic systems. The problem of realizing an Nn_o×Nn_i proper rational transfer matrix as an n_i-input n_o-output N-periodic discrete-time system is studied. An algorithm for obtaining periodic realizations which have a minimal number of states is proposed. The result can also be used to remove any redundant states that exist in a periodic system