On observability and reachability in a class of discrete-time switched linear systems

We study the class of switched linear systems with constant dynamics, i.e., with switching in only the measurement or control matrices (which correspond to plants with several sensory and actuation modes), and establish that the length of the shortest mode path achieving observability or reachability, if one exists, is at most the square of the dimension of the state space. This not only proves that observability/reachability is decidable for such systems, but also gives a direct way of finding the observable/reachable mode path.