On a class of time-varying behaviors

We study a class of time-varying systems that we encounter when we look into decomposition of behaviors. This class is the set of behaviors that are themselves of polynomials in time, with coefficients as time-invariant behaviors. Operators that have such behaviors as their kernels are studied. It turns out that autonomous behaviors allow kernel representations of this kind. We are led to the study of skew polynomial ring as the underlying ring for such operators.