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

Abstract

AbstractThis 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 δ ($\delta >0$ δ > 0 ) to make an unstable SDEwMJ become stable. It is proved that the delay δ is bounded by a constant δ̄. Moreover, an implicit lower bound for $\bar{\delta ,}$ δ , ¯ 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.