A. Bemporad, G. Ferrari-Trecate, and M. Morari. Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. Autom. Contr. , 45(10):1864--1876, 2000. Link to IEEE Trans. AC
In this paper we prove, in a constructive way, the equivalence betweenpiecewise affine systems anda broad class of hybrid systems described byinteracting linear dynamics, automata, and propositional logic.By focusing our investigation on the former class, we show through counterexamples thatobservability and controllability properties cannot be easily deduced from those of thecomponent linear subsystems. Instead, we propose practical numerical tests based onmixed-integer linear programming.