Active mode observability of switching linear systems

Active 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 active mode observation problem consists in determining control sequences (discerning control sequences) that allow to reconstruct the switching sequence on the basis of the observations. The presence of unknown but bounded noises affecting both the system and measurement equations is taken into account. A general condition is derived that characterizes discerning controls in a finite-horizon setting. Such a result is extended to the infinite-horizon case in order to derive "persistently discerning" control sequences. A numerical example is reported to clarify the approach.