Hybrid dynamical systems are composed of continuous-time dynamical parts, mixed with event-driven parts. Most of the time, both parts are designed separately using specific techniques of each domain, and integrated a posteriori in an application-specific manner. This approach is restrictive in that it does not exhibit a hybrid global model of the designed system, that would though be required for analysis and behavior-checking to take place. In this paper, we discuss and illustrate our approach of hybrid systems modeling, that is based on the obvious statement that both domains (dynamical and event-driven) must be clearly considered in an integrated manner from the very beginning of the design.
In our example, we exhibit a draft formal framework for hybrid system modeling, that would allow for verification techniques. For that purpose, we take advantage of the recently developed techniques and tools, in both areas. The numerical computation laboratory - matlab - that we chose for the dynamical system part design, fits perfectly with our goals. But the reactive synchronous language chosen - Esterel - , if it actually fits with the event-driven part specification, exhibits some weaknesses when dealing with data and values, that are needed when interfacing both parts together.