A new integral inequality method is put forward to analyze the general decay stability for Markovian switching neutral stochastic functional differential systems. At first, in order to get around the dynamic analyses difficulty induced by the coinstantaneous presence of neutral term, Markovian switching and Brownian motion noise, an new integral inequality as a powerful tool is gained. Then, based on the integral inequality, general decay stability in the sense of $p$th($p>0$) moment and the almost sure can be taken out by utilizing the nonnegative semimartingale convergence theorem and Lyapunov stability theory. The obtained results can be especially applied to two special types of neutral stochastic differential systems that have been studied in the literature. Finally, an example has been performed to verify the obtained analytical results.

提出了一种新的积分不等式方法，用于分析马尔可夫切换中立型随机泛函微分系统的一般衰减稳定性。首先，为了解决因中立项，马尔科夫切换和布朗运动噪声的同时存在而引起的动力学分析困难，获得了新的积分不等式作为有力的工具。然后，基于积分不等式，一般意义上的衰变稳定性$p$th（$p>0$利用非负半mart收敛定理和Lyapunov稳定性理论可以得出矩和几乎确定的矩。所获得的结果可以特别地应用于已经在文献中研究的两种特殊类型的中性随机微分系统。最后，通过一个例子验证了所获得的分析结果。