# Handbook of Hybrid Systems Control by Jan Lunze download in iPad, pdf, ePub

De Schutter Autonomous state jumps These constitute the second hybrid phenomenon. In the tank system the level controller is equipped with a safety switch-off.

However, due to the inherent complexity of hybrid systems, many issues still remain unsolved at present, at least at the scale needed for industrial applications. The current status of hybrid systems theory is surveyed in this handbook, which can be used as a starting point for future developments in this appealing and challenging research domain. This is illustrated in Fig. The following example also illustrates event-driven switching.

Also in this domain hybrid systems theory plays an essential role as a foundation to understand the behavior of these complex systems. The tank in the right part of Fig.

The hybrid system models explained in Part I of this handbook combine both ideas. Indeed, continuous models represented by differential or difference equations, as adopted by the dynamics and control community, have to be extended to be suitable for describing hybrid systems.

The trajectories of hybrid systems are partitioned into several time intervals. The changes of the discrete state q are determined by the continuous state T and different conditions on T might trigger the change of the discrete state e. Theory, Tools, Applications, ed. The switching can also be invoked when the continuous state x reaches some switching set S.

Many physical processes, exhibiting both fast and slow changing behaviors, can often be well described by using simple hybrid models. This is an example of time-driven switching. For instance, in the thermostat example these transition times were determined by the temperature T reaching the values Tmin or Tmax state events. Within one single system, many subsystems interact through communication networks.

An autonomous jump set is a set S on which a state jump is invoked Fig. Indeed, as the impacts occur at a much smaller time scale than the unconstrained motion, the behavior can be described well by introducing discrete events and actions in a smooth model.

The dependence of the vector field upon the state can be simply written down. It shows that the evolution consists of smooth phases in which the discrete state remains constant and the continuous state changes continuously. The system depicted in Fig. An important characteristic of hybrid systems lies in the fact that this pair influences the future behavior of the system. To provide some insight in this interaction, let us consider the following example.

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