On stabilization for discrete linear time-varying systems

In this paper, we consider the stabilization problem for discrete linear time-varying systems in an operator-theoretic framework. By using the complete finiteness of a certain discrete nest algebra, we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation. This result extends the Youla parametrization theorem by only requiring a strong left or a strong right representation but not both. The strong stabilization problem is also discussed.