Stabilization of stochastic regime-switching Poisson jump equations by delay feedback control

This paper is concerned with the stabilization of stochastic regime-switching Poisson jump equations (also known as stochastic differential equations with Markovian switching and Poisson jumps, abbreviated as SDEwMJs). The aim of this paper is to design a feedback controller with delay delta (delta > 0) to make an unstable SDEwMJ become stable. It is proved that the delay delta is bounded by a constant (delta) over bar. Moreover, an implicit lower bound for (delta) over bar, which can be computed numerically, is provided. As a product, the almost sure exponential stability of the controlled SDEwMJ is obtained. Besides, an example is given to demonstrate the theoretical results.