Abstract
This paper develops the realization theory for linear periodic continuous-time systems. The substantial difficulty in the period-specific realization problem is that there may be no solution among linear periodic systems whose dimensions are equal to the order of a given weighting pattern matrix, in sharp contrast with realization problems for general linear time-varying systems or linear time-invariant systems. This paper proves the existence of period-specific realizations even when there exists no realization with dimension equal to the order of the weighting pattern matrix. It is finally shown that the realizations obtained in this paper have a minimal dimension among all of possible realizations with a specific period of time.
