Controllability of a class of bimodal discrete-time piecewise linear systems

In this paper we will provide full algebraic necessary and sufficient conditions for the controllability/reachability/null controllability of a class of bimodal discrete-time piecewise linear systems including several instances of interest that are not covered by existing works which focus primarily on the planar case. In particular, the class is characterized by a continuous right-hand side, a scalar input and a transfer function from the control input to the switching variable with at most two zeroes whereas the state can be of any dimension. To prove the main result, we will make use of geometric control theory for linear systems and a novel result on controllability for input-constrained linear systems with non-convex constraint sets.