In this paper, the finite-time stability in mean for the uncertain fractional order linear time-invariant discrete systems is investigated. First, the uncertain fractional order difference equations with the nabla operators are introduced. Then, some conditions of finite-time stability in mean for the systems driven by the nabla uncertain fractional order difference equations with the fractional order 0 < ν < 1 are obtained by the property of Riemann–Liouville-type nabla difference and the generalized Gronwall inequality. Furthermore, based on these conditions, the state feedback controllers are designed. Finally, some examples are presented to illustrate the effectiveness of the results.

中文翻译：

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NABLA 不确定分数阶线性差分系统均值的有限时间稳定性

本文研究了不确定分数阶线性时不变离散系统的均值有限时间稳定性。首先，介绍了带有nabla算子的不确定分数阶差分方程。然后, 由具有分数阶的 nabla 不确定分数阶差分方程驱动的系统的平均有限时间稳定性的一些条件0 < ν < 1由黎曼-刘维尔型 nabla 差分和广义 Gronwall 不等式的性质得到。此外，基于这些条件，设计了状态反馈控制器。最后，给出了一些例子来说明结果的有效性。