Observability and controllability of piecewise affine and hybrid systems

In this paper we prove, in a constructive way, the equivalence between
piecewise affine systems and
a broad class of hybrid systems described by
interacting linear dynamics, automata, and propositional logic.
By focusing our investigation on the former class, we show through counterexamples that
observability and controllability properties cannot be easily deduced from those of the
component linear subsystems. Instead, we propose practical numerical tests based on
mixed-integer linear programming.