A special class of hybrid systems is considered, whose state space is a cross-product space of a euclidean space and a finite-state space. Such models may be used to represent systems subject to known abrupt parameter variations, such as commu- tated networks. They may also be used to approximate some types of time-varying systems. Controllability, observability and stability of hybrid systems are inves- tigated. In particular, a necessary and sufficient algebraic condition, a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived. Moreover, a simple sufficient stability condition is provided.