Necessary and sufficient conditions for robust observability of a class of discrete-time uncertain systems

This paper considers the problem of robust observability for a class of uncertain discrete-time systems. The uncertainty is modelled via a sum quadratic constraint. A necessary and sufficient condition for robust observability is presented in terms of existence of a solution to a Riccati difference equation. The set of possible initial states given measurements over a finite number of sampling periods is shown to be an ellipsoid. The main result of this paper can be considered as an extension to the standard notion of observability for discrete-time, linear time-varying systems.