Controllability of Linear Systems With Switching Delays

We consider discrete-time linear time-invariant (LTI) systems with state feedback, where the actuation signal is subject to switching propagation delays, due to, e.g., routing in a multi-hop communication network. We show how to model these systems as pure switching linear systems and provide an algorithm for robust stability analysis. Next, we turn to the design problem and provide an algorithm that computes in a finite number of steps the look-ahead knowledge of the delays (i.e., routing) necessary to achieve controllability and stabilizability. This generalizes well known controllability criteria for LTI systems.