This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ϵ_i‐free but involving its bound are developed by constructing an ϵ_i‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.

中文翻译：

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具有马尔可夫跳的奇摄动系统的稳定性和稳定性

本文重点讨论奇摄动跳跃系统的稳定性和稳定性问题。此处，奇异摄动参数（SPP）也具有马尔可夫切换，并且满足任何具有预定义的正边界的参数。首先，稳定的条件表示ε_我-free但涉及其必然通过构建一个开发ε_我依赖的Lyapunov函数。然后，提出了一种基于SPP的状态反馈稳定控制器的方法，其条件根据线性矩阵不等式给出。此外，还考虑了有关确定性SPP的一些特殊情况。最后，两个实际例子被用来证明所提出方法的有效性和优越性。