抄録
For linear periodic discrete-time (LPDT) plants, the closed-loop systems are linear periodic in general when periodic compensation is adopted. However, in some cases, the closed-loop system can be made to be linear time-invariant (LTI) by choosing the compensator suitably. In these cases, we say the plant is LTI model realizable.
In this paper, we consider the LTI model realization problem of LPDT systems (period: N) following the transfer function approach. Defining the transfer function of LPDT plant, we give a special coprime factorization for the transfer function, in which every factor is lower triangular at the origin. Then the class of all LPDT stabilizing compensators can be parametrized similar as YJB parametrization, with free parameters chosen being lower triangular at the origin. Using such stabilizing compensators, we show the necessary and sufficient condition for realizing the closed-loop as LTI, and give the class of all realizable LTI models.
We show also that, the class of all realizable LTI models by N-periodic compensation is same with that by pN-periodic compensation (p: arbitrary positive integer).
