Closed Form Solutions of Hybrid Systems

In this paper we present a new symbolic approach to hybrid systems Hybrid systems are systems con taining both continuous and discrete changing quantities We model hybrid systems using hybrid automata Hybrid automata extend the classical notion of nite state machines by combining di erential equations to model the dynamic behavior of systems with a nite control In contrast to other approaches we consider a hybrid automata as a generalization of di erential equations and develop the notion of a symbolic closed form solution of a hybrid automata A closed form solution is an expression which gives the value of the quantities in question as a function of design parameters and time These solutions allow us to perform the veri cation of design properties We were able to detect design constrains on control systems that other methods fail to detect This paper gives the basic de nitions algorithms and an example to demonstrate the advantage of the proposed approach