Analysis of Singularly Perturbed Stochastic Hybrid Systems

This paper considers a singularly perturbed hybrid system whose state equations are governed by a stochastic switching process, which is singularly perturbed and is modeled as a near decomposable continuous time finite state Markov chain (FSMC). The decomposition of the system and the switching process together into slow and fast subsystems is investigated. An approximate model for the slow subsystem over the interval of fast transitions within each group is derived and the mean-squared error between the model and the actual subsystem is quantified. The stability of the slow mode subsystem is studied and two stability criteria are introduced. The behavior of the fast subsystem depending on the relative size of perturbation parameters is analyzed. Finally an example is used to illustrate the aforementioned techniques.