This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama (EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.

本文研究了一类具有不可区分模式的采样数据非线性马尔可夫切换系统的镇定问题。为了处理难以区分的模式，作者通过模式聚类方法重构了原始模式空间，形成了一个新的合并马尔可夫切换系统。通过指定合并系统的Euler-Maruyama（EM）近似离散时间模型与原始Markov切换系统的精确离散时间模型之间的差异，作者证明了为合并系统设计的采样数据控制器基于其EM近似，可以在均方意义上以指数方式稳定原始系统。最后，通过数值例子说明了该方法的有效性。