Modeling and analysis of hybrid systems: a new approach integrating Petri nets and differential equations

Hybrid technical systems combine discrete-state event-driven and continuous-state time-driven behaviour. In this contribution, a general modeling formalism for such systems is proposed. The discrete subsystem is represented by an interpreted Petri net. In addition to external continuous inputs, discrete variables dependent on the net marking affect the continuous subsystem which is a time-driven state space model. Limit violations of particular continuous state variables as well as external binary inputs are interpreted as events and change the discrete state of the system. In view of the analysis of hybrid technical systems reachability and stability are defined. The modeling method is applied to a mixing tank