Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems

Abstract

For an unstable Markov jump stochastic differential system (MJ-SDS) with high nonlinearity, can one introduce a discrete feedback control to stabilize it? This question has been well answered for the case of the feedback control derived from discrete state observations, in the form of H∞ stabilization and exponential stabilization. Whereas, the existing theory can not tackle the non-autonomous systems and do not consider the factor of discrete mode observations, which are the motivations of this paper. Fortunately, for an unstable non-autonomous MJ-SDS, the feedback control, originated from discrete observations of system state and system mode, is well designed to stabilize it not only in the sense of exponential decay rate but also of polynomial decay rate and even general decay rate. Thereinto, the designing rule of discrete feedback control is given as well.