ABSTRACT This paper addresses the design of a non-fragile exponential polynomial observer for a class of fractional-order nonlinear systems. Existence of the observer is proven and a sufficient condition for the stability of the state estimation error dynamics with a predetermined exponential convergence rate is derived employing the Lyapunov stability theorem. The exponential stability criterion is proposed in the form of linear matrix inequalities (LMIs). Moreover, some numerical examples have been provided to illustrate the effectiveness of the proposed approach. The synchronisation of fractional-order Lorenz systems has been investigated using the proposed method. Then, the proposed method has been applied to the chaotic communication problem of fractional-order chaotic systems with four scroll attractors.

中文翻译：

---

一类非线性分数阶系统的非脆弱指数多项式观测器设计在混沌通信和同步中的应用

摘要 本文讨论了一类分数阶非线性系统的非脆弱指数多项式观测器的设计。证明了观测器的存在性，并利用李雅普诺夫稳定性定理推导出具有预定指数收敛速率的状态估计误差动力学稳定性的充分条件。指数稳定性准则以线性矩阵不等式（LMI）的形式提出。此外，还提供了一些数值例子来说明所提出方法的有效性。已经使用所提出的方法研究了分数阶洛伦兹系统的同步。然后，将所提出的方法应用于具有四个滚动吸引子的分数阶混沌系统的混沌通信问题。