Feedback control of singularly perturbed stochastic hybrid systems

This paper addresses the stability properties and stabilization schemes for a class of stochastic hybrid systems. Such systems switch among a finite number of linear singularly perturbed system models with switched behavior governed by a nearly completely decomposable finite state Markov chain. The stability properties of the decoupled slow subsystem, fast subsystem, and the overall system are examined. Linear switching stabilization schemes with perfect as well as imperfect Markov chain detectors are developed to stabilize the overall system. Two examples are provided to illustrate the stabilization schemes