General Theory of Multivalued Differential Automata
Alexey S. Matveev, Andrey V. Savkin · Birkhäuser Boston eBooks · 2000
In this chapter, we introduce a general class of hybrid dynamical systems that operate as follows. While the discrete state remains unchanged, the continuous one obeys a definite ordinary differential equation. Transition to another discrete state causes an alteration of this equation. The discrete state keeps its value, while the continuous one remains in a certain specific region and evolves as soon as this region is left. Furthermore, we introduce a number of basic notions related to the above class. Among them, there is, for example, that of the invariant domain, as well as of deterministic and well-posed systems. In particular, we provide mathematically rigorous definitions of some notions that were employed in Chapter 2. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.