A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

This paper deals with the total observability problem of discrete-time linear time-varying systems. In particular, a review and suitable analysis of the state-of-the-art of this emerging area are provided. Subsequently, the total observability problem of discrete-time linear time-varying systems is transformed into the one of checking the rank of a convex sum of matrices. As a result, a new total observability test is proposed, along with a suitable computational strategy. The final part of this paper shows examples regarding observability analysis that clearly exhibit the benefits of using the proposed approach.