IJCAS

In this paper, the problems on the exponential stability in p-th (p ≥ 2)-moment and the almost sure exponential stability for neutral stochastic differential delay equation with Markovian switching and impulses are analyzed. By establishing an impulsive delay integral inequality, the Lyapunov theorem on the exponential stability in p-th (p ≥ 2)-moment is given. Then, by using the Borel-Cantelli lemma, the almost sure exponential stability theorem is also proved. Two major advantages of these two results are that the differentiability or continuity of the delay function is not required, and that while considering the concerned problem, the difficulty coming from the simultaneous presence of the neutral item, the impulsive disturbance and the stochastic perturbations is overcome. An example is provided to examine the effectiveness and potential of the theoretic results obtained. "

Keywords: Almost sure exponential stability, exponential stability, impulses, Markovian switching, neutral stochastic differential delay equation.