Stabilizability and detectability of discrete-time time- varying systems

In this paper we introduce some notions of stabilizability and detectability for discrete time-varying systems. These concepts are introduced by making state-space decompositions of the system. This allows an intuitive interpretation and shows the difficulties which occur if one tries to derive general stabilizability and detectability properties. Moreover, we show by means of a counterexample that the notions ofunifonn stabilizability and unifonn detectability, as defined by Anderson and Moore, do not imply stabilizability respectively detectability of the system.