On the Controllability and Observability of Hybrid Systems

This paper considers a special class of hybrid systems, whose state space is a cross-product space of an Euclidean space and a finite-state space. Such models may be used to represent systems subject to known abrupt parameter variations, such as commutated networks. They may also be used to approximate some types of time-varying systems. The paper investigates controllability, observability, and stability of hybrid systems. In particular, it derives a necessary and sufficient algebraic condition, a simple algebraic criterion, and a computationally simple algebraic sufficient test for controllability and observability. Moreover, it provides a simple sufficient stability condition.