Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching

Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.