This article deals with the problem of stochastic stability for a class of discrete-time Markovian jump singular systems. A time-dependent coordinate transformation is provided, under which an equivalent form of the original Markovian jump singular systems can be obtained. This equivalent form not only shows the inherent state jump behavior at the switching instants, but also plays an important role in the stochastic stability analysis. Constructing a supermartingale over some σ\sigma-algebra together with the property of conditional expectation, a necessary and sufficient condition is established to ensure that the equilibrium point of the underlying system is exponentially stable in mean square. Two numerical examples are given to illustrate the effectiveness of the developed results.

中文翻译：

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基于超鞅方法的离散时间马尔可夫跳跃奇异系统随机稳定性的新判据


本文讨论一类离散时间马尔可夫跳跃奇异系统的随机稳定性问题。提供了一种与时间相关的坐标变换，在该变换下可以获得原始马尔可夫跳跃奇异系统的等效形式。这种等效形式不仅显示了切换瞬间的固有状态跳跃行为，而且在随机稳定性分析中发挥着重要作用。在某些 σ\sigma 代数上构造超鞅，结合条件期望的性质，建立了确保基础系统的平衡点均方指数稳定的充分必要条件。给出了两个数值例子来说明所开发结果的有效性。