A. Bemporad, G. Ferrari-Trecate, and M. Morari. Observability and controllability of piecewise affine and hybrid systems. Proc. 38th Conference on Decision and Control , 4:3966--3971, 1999. Phoenix, Arizona, US, 7-10 December.
In this paper we prove, in a constructive way, the equivalencebetween hybrid and piecewise affine systems. By focusing ourinvestigation on the latter class, we show through counterexamplesthat observability and controllability properties cannot be easilydeduced from those of the component linear subsystems. Instead, wepropose practical numerical tests based on mixed-integer linearprogramming.