A low‐dimensional realization algorithm for periodic input/output behavioral systems

The state-space realization of linear systems is utmost importance in theory. After the problem for time-invariant case was solved, particular attention paid to periodic systems. Recently, such have regained importance, instance, context coding theory where convolutional encoders play an important role. majority contributions within this area only concern transfer functions (or impulse responses), thus excluding input/output without coprime representations. By end eighties last century, Jan C. Willems suggested approach (nowadays known as behavioral approach) that considers a wider class and allows overcome drawback. According approach, central object system its behavior which consists all signals satisfy laws (also called trajectories). Consequently, with representation not contains more trajectories than set defined by function. Our work takes fact into account. In previous research conducted authors, some results on were obtained, which, despite their are conservative respect dimension obtained realizations. paper, we revisit give further insight question. This derive new up algorithm compute low-dimensional