Overview of hybrid dynamic systems

Dynamical systems are generally classified according to whether they evolve continuously, in which case they are called continuous-time dynamical systems, or discretely, in which case they are called discrete-time dynamical systems. These two classes of systems have been studied extensively in the literature, but usually independently (see for example , ), using differential equations for continuous systems and difference equations for discrete systems. There are, however, many physical systems that combine both types of behavior, such as digitally controlled mechanical systems, or electronic circuits that combine analog and digital components. Similarly, dynamic systems with impacts and event-based systems, to name but two examples, require an adequate combination of behaviors described by differential equations and behaviors described by difference equations. Social networks and their studies can be seen as another field of application for hybrid dynamical systems (see, for example, ). For more details and examples, the reader can consult Chapter 1 of .

Reset control systems are another class of systems that mix continuous dynamics and discrete events . They were introduced in the 1950s with the idea of exploiting reset to improve the behavior of a system controlled with a simple linear controller