非线性奇异系统的相关问题研究

doi:10.12677/PM.2022.125099

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非线性奇异系统的相关问题研究
Research on Some Related Problems of Nonlinear Singular Systems

DOI: 10.12677/PM.2022.125099, PDF, HTML, 下载: 278 浏览: 502
作者: 彭思瑶：浙江师范大学，浙江金华
关键词: 非线性奇异脉冲系统；L₂-增益；线性矩阵不等式；非线性混合奇异脉冲切换系统；Nonlinear Singular Impulse System； L₂-Gain； LMI； Nonlinear Mixed Singular Impulse Switched System

摘要: 奇异系统，也称为描述系统，广义状态空间系统，隐式系统，微分代数系统或半状态系统。它在电力系统，经济系统，及电子网络等领域有着广泛的应用，很多问题都可以以奇异系统作为背景进行研究。奇异系统的理论研究经过几十年的发展，已经取得了一些令人瞩目的成果，并且应用也十分广泛，譬如在电气，机械系统，无损传输线，柔性臂控制机器人等实际系统中都有广泛应用。本文主要运用平均脉冲间隔和线性矩阵不等式的方法讨论非线性奇异脉冲切换系统的指数稳定性与 L₂-增益。

Abstract: Singular systems, also known as description systems, generalized state space systems,implicit systems, diﬀerential algebraic systems or semistate systems. It has a wide range of applications in power systems, economic systems, and electronic networks. Singular systems can be studied in the background. The theoretical study of singular systems has been developed for several decades. Some remarkable results have been obtained, and the application is also very wide, such as in electrical, mechanical systems, lossless transmission line, ﬂexible arm control robot and other practical systems. In this paper, the sum of average pulse intervals is mainly used. The exponential stability and L₂-gain of nonlinear singular impulsive switched systems are discussed using linear matrix inequality (LMI) method.

文章引用：彭思瑶. 非线性奇异系统的相关问题研究[J]. 理论数学, 2022, 12(5): 894-910. https://doi.org/10.12677/PM.2022.125099

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