Minimal Periodic Realizations of Transfer Matrices

Periodic controllers designed based on the so-called lifting technique are usually represented by trasfer matrices. Real-time operations require that the controllers be implemented as periodic system. We study 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. We propose an algorithm to obtain periodic realizations which have a minimal number of states. The result can also be used to remove any redundant states that exist in a periodic system.