Stabilizability and detectability of discrete-time time-varying systems

Stabilizability and detectability for discrete time-varying systems are discussed. These concepts are introduced by decomposing the state space of the system into three orthogonal subspaces. This allows an intuitive interpretation and shows the difficulties which occur when general stabilizability and detectability properties are derived. A counterexample is given to show that a previously published claim that the time-varying discrete-time Kalman filter is exponentially stable under the conditions of uniform stabilizability and uniform detectability is incorrect