Editing Hybrid system (section)

{{technical|date=May 2025}}
{{Short description|Dynamical system that exhibits continuous and discrete dynamic behavior}}
A '''hybrid system''' is a [[dynamical system]] that exhibits both continuous and discrete dynamic behavior&nbsp;– a system that can both ''flow'' (described by a [[differential equation]]) and ''jump'' (described by a [[Finite-state machine|state machine]], [[Automata theory|automaton]], or a [[difference equation]]).<ref>{{Citation |last=Branicky |first=Michael S. |title=Introduction to Hybrid Systems |date=2005 |url=https://doi.org/10.1007/0-8176-4404-0_5 |work=Handbook of Networked and Embedded Control Systems |pages=91–116 |editor-last=Hristu-Varsakelis |editor-first=Dimitrios |place=Boston, MA |publisher=Birkhäuser |language=en |doi=10.1007/0-8176-4404-0_5 |isbn=978-0-8176-4404-8 |access-date=2022-06-08 |editor2-last=Levine |editor2-first=William S.|url-access=subscription }}</ref> Often, the term "hybrid dynamical system" is used instead of "hybrid system", to distinguish from other usages of "hybrid system", such as the  combination [[neural net]]s and [[fuzzy logic]], or of electrical and mechanical drivelines. A hybrid system has the benefit of encompassing a larger class of systems within its structure, allowing for more flexibility in modeling dynamic phenomena.

In general, the ''state'' of a hybrid system is defined by the values of the ''continuous variables'' and a discrete ''mode''. The state changes either continuously, according to a [[Flow (mathematics)|flow]] condition, or discretely according to a ''control graph''. Continuous flow is permitted as long as so-called ''invariants'' hold, while discrete transitions can occur as soon as given ''jump conditions'' are satisfied. Discrete transitions may be associated with ''events''.