Finite Divergence

Real-time and hybrid systems have been studied so far under the assumption of finite variability. In this paper, we consider models in which systems exhibiting finite divergence can also be analysed. In such systems, the state of the system can change infinitely often in a finite time. This kind of behaviour arises in many representations of hybrid systems, and also in theories of nonlinear systems. The aim is to provide a theory where pathological behaviour such as finite divergence can be analysed-if only to prove that it does not occur in systems of interest. Finite divergence is studied using the framework of duration calculus. Axioms and proof rules are given. Patterns of occurrence of divergence are classified into dense divergence, accumulative divergence and discrete divergence by appropriate axioms. Induction rules are given for reasoning about discrete divergence