Simplified algorithm of the transition relation in the hybrid system verification

In the hybrid system verification, the flow pipe approximation method is utilized to compute reachable states from initial states in order to obtain the transition relation of the approximate quotient transition system. According to the character of the linear time-invariant system and the properties of convex polyhedron, the evolving rules of the reachable set of the system are presented and proved. By means of these rules, the computation of the transition relation in the hybrid system verification is simplified and the algorithm by combining vertices simulation and flow pipe approximation is presented. Finally, the temperature control system of atmospheric pressure oven is taken as an example to illustrate the computation process of the quotient transition relation by the presented method. It is also compared with the flow pipe approximation method.