Spectral conditions for the reachability of discrete-time conewise linear systems

This paper studies the reachability problem for discrete-time conewise linear systems. Controllability of continuous-time conewise linear systems has already been studied in the literature and admits elegant spectral characterizations that resemble the well-known Popov-Belevitch-Hautus test for linear systems. However, the techniques that are employed for continuous-time systems are not applicable in the context of discrete-time due to the lack of convexity of a certain set of reachable states. To overcome this obstacle, we employ a combination of methods from geometric control theory and convex analysis and provide spectral conditions for the reachability of discrete-time conewise linear systems.