论文标题
与Mittag-Leffler内核的分数非线性系统的稳定性和国家观察家的设计
Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers
论文作者
论文摘要
Atangana和Baleanu提出了一种新的分数衍生物，该衍生物具有非本地且无单一的Mittag-Leffler内核，以解决分数演算领域的研究人员提出的一些问题。这种新的衍生物更好地描述了非本地动力学系统的基本方面。我们提供了有关Lyapunov稳定性理论的一些结果，尤其是使用Atangana-Baleanu衍生物建模的分数系统的Lyapunov直接方法，以及一些有助于开发理论分析的重要不平等。作为控制理论中的应用，对线性和非线性分数系统提出了一些状态估计的算法。
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.
