On p th moment exponential stability of stochastic differential equations with Markovian switching and time-varying delay

Abstract

In this paper we discuss the problem of pth moment exponential stability for general nonlinear stochastic differential equations with Markovian switching and time-varying delay. By using the Lyapunov function, the stochastic analysis technique and the generalized Halanay inequality, some novel sufficient conditions on pth moment exponential stability of stochastic differential equations with Markovian switching and time-varying delay are derived. The results obtained in this paper are completely new and modify and improve some known results. Moreover, two numerical examples are also provided to demonstrate the effectiveness and applicability of the theoretical results. The aim of this paper is to investigate pth moment exponential stability of general nonlinear stochastic differential equations with Markovian switching and time-varying delay.