Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe essential aspects of non-local dynamical systems. We present some results regarding Lyapunov stability theory, particularly the Lyapunov Direct Method for fractional-order systems modeled with Atangana-Baleanu derivatives and some significant inequalities that help to develop the theoretical analysis. As applications in control theory, some algorithms of state estimation are proposed for linear and nonlinear fractional-order systems.

中文翻译：

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带有 Mittag-Leffler 核的分数非线性系统的稳定性和状态观测器的设计

Atangana 和 Baleanu 提出了一种新的具有非局部和非奇异 Mittag-Leffler 核的分数阶导数，以解决分数阶微积分领域研究人员提出的一些问题。这种新的导数更好地描述了非局部动力系统的基本方面。我们提出了一些关于李雅普诺夫稳定性理论的结果，特别是用 Atangana-Baleanu 导数和一些有助于发展理论分析的重要不等式建模的分数阶系统的李雅普诺夫直接方法。作为在控制理论中的应用，针对线性和非线性分数阶系统提出了一些状态估计算法。