OBSERVABILITY OF DISCRETE TIME LINEAR SWITCHING SYSTEMS1

In previous work, we defined observability (detectability) for continuous-time linear switching systems, as the possibility of reconstructing (respectively, asymptotically reconstructing) the hybrid state of the system from the knowledge of the hybrid outputs for a suitable choice of the control input. In this paper, we address observability for discrete-time linear switching systems. While in continuous-time linear switching systems detection is possible in an arbitrarily small amount of time, in the discrete time case it requires a finite, non-zero number of instants. We derive a sufficient testable condition for the reconstruction of the hybrid state.