Abstract
Realization theory for linear periodic systems with real coefficients is developed in this paper. It is a well-known fact that a weighting pattern matrix is realizable as a linear periodic system if and only if the weighting pattern matrix is separable and periodic. This fact, however, can not handle a reasonable question when a weighting pattern matrix can be realized as a linear periodic system with a specific period of time. This paper attacks the question to derive a new necessary and sufficient condition for the period-specific realizability. Under the condition, a linear periodic realization for a given weighting pattern matrix is obtained. The realization procedure proposed in this paper essentially consists of integrations over a prescribed interval and computations of a real logarithm of a matrix. Thus, the procedure provides a transparent connection between weighting pattern matrices and their state-space representations.
