Event-driven discontinuities for continuous-time systems

Abstract

Consideration is given to systems for which the observed behavior can exhibit occasional discontinuous changes of mode in the course of normal (autonomous) evolution. This can occur by design, as in the case of modal control under feedback; as the result of involvement of discontinuous elements as relays; or as an effect of discretization or digital circuitry. Such system also arise in the modeling of natural systems (e.g. neural firing), where they can be regarded as being associated with unmodeled fast time scales. Each of these situations leads to a limit problem, for which the frameworks of the analyses are sketched.<>