Controllability with a Finite Data-Rate of Switched Linear Systems

In this work, we argue that the usual notion of controllability is unfit for systems that operate with finite data-rate constraints. We deal with this issue by defining a new concept of controllability with finite data-rate. Then, we specialize our discussion to the case of switched linear systems. We state a necessary condition and a sufficient condition for our new controllability notion to hold. Next, we take advantage of the switched linear system's structure to present a simple sufficient condition for controllability with finite data-rate that only involves the controllable subspace of the individual modes and some mild assumptions about the switching signal that guarantee that our sufficient condition holds. We also present another sufficient condition for systems that activate some controllable mode often enough. In particular, we illustrate the power of this result by deriving relations between the sampling time and the Average Dwell-Time (ADT) of the switching signal that guarantee that the switched system is controllable with finite data-rate. Finally, we discuss the gap between the necessary and the sufficient conditions and show that the sufficient condition is not necessary.