Stochastic hybrid systems models for performance and reliability analysis of power electronic systems

Abstract

Stochastic hybrid systems (SHS) are a class of stochastic processes with a state space composed of a discrete state and a continuous state. The transitions of the discrete state are random, and the rates at which these transitions occur are, in general, a function of the value of the continuous state. For each value that the discrete state takes - referred to subsequently as modes of the system - the evolution of the continuous state is described by a stochastic differential equation. The vector fields that govern the evolution of the continuous state in each mode depend on the operational characteristics of the system in that mode. Reset maps associated with mode transitions define how the discrete and continuous states map into posttransition discrete and continuous states.