We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it i...

Hybrid automata have been proposed as a language for modelling and analysing the interaction of digital and analogue dynamics in embedded computer systems. In this paper, hybrid automata are studied from a dynamical systems perspective. Extending earlier work on conditions for local existence and uniqueness of executions of hybrid automata, we characterise a class of hybrid automata whose execu...

Fault diagnosis is a challenging task in the control of Hybrid Systems. In this work we introduce the notion of diagnosability of Hybrid Systems in the framework of Hybrid Input Output Automata (HIOA). We present a methodology for detection of faults imposing the conditions for a Hybrid System to be diagnosable. This approach is applicable to a wide rage of systems since Hybrid Systems involve ...

A uni ed approach to decidability questions for veri cation algorithms of hybrid systems is obtained by the construction of a bisimulation. Bisimulations are nite state quotients whose reachability properties are equivalent to those of the original in nite state hybrid system. In this paper, we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant...