广义 Persidskii 系统的环形短时稳定性条件
On annular short-time stability conditions for generalized Persidskii systems
AI总结：
针对含本质有界输入的广义 Persidskii 系统，提出基于线性矩阵不等式的环形短时稳定性等条件，并通过递归神经网络验证其实用性。
摘要：
本文研究有限时间区间内具有本质有界输入的广义 Persidskii 系统的轨迹行为评估。同时，介绍了一般非线性系统的环形稳定和输出环形稳定概念。针对一类 Persidskii 系统，提出了环形短时稳定性、非零初始状态下的短时有界性、环形稳定以及输出环形稳定的条件。这些条件基于线性矩阵不等式的验证。对递归神经网络的应用说明了所提出概念和条件的实用性。
英文摘要：
This paper studies the trajectory behavior evaluation for generalized Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced. We propose conditions for annular short-time stability, short-time boundedness with a nonzero initial state, annular settling, and output annular settling for a class of Persidskii systems. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions.
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