A Spectral Characterization of Controllability for Linear Discrete-Time Systems with Conic Constraints

In this paper, we generalize all previously known results on the controllability of discrete-time linear systems with conic input and/or state constraints. In addition, we single out two cases of the problem which did not appear in the literature before. We provide a characterization for the first one of these new cases. For the second newly introduced case, we show that it is rare and pathological. Moreover, we show that the classical results cannot be extended to this last pathological case. These results altogether lead to an almost complete spectral characterization of controllability for discrete-time linear systems with conic input and/or state constraints.