Active mode observation of switching systems based on set-valued estimation of the continuous state

Mode observability is addressed for a class of discrete-time linear systems that may switch in an unknown and unpredictable way among different modes taken from a finite set. The possible a priori knowledge on the continuous state of the system and the presence of unknown but bounded noises affecting both the system and the measurement equations are explicitly taken into account. The mode observation is performed ‘actively’: control sequences (discerning control sequences) are searched, which allow to identify the switching sequence on the basis of the observations. Conditions that characterize discerning controls in a finite-horizon setting are obtained. Moreover, a procedure is proposed in order to derive ‘persistently discerning’ control sequences (over an infinite horizon). A numerical example is reported to clarify the approach.