一类不确定时滞系统的非线性保性能控制  

NONLINEAR GUARANTEED PERFORMANCE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

作　　者：李雨欣 王天成 徐放 Li Yuxin;Wang Tiancheng;Xu Fang(School of Mathematics and Statistics Science,Ludong University,264025,Yantai,Shandong,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264025

出　　处：《山东师范大学学报(自然科学版)》2024年第4期325-330,共6页Journal of Shandong Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(62373179)。

摘　　要：本文主要探讨一种含不确定时滞系统的非线性保性能控制问题。基于李雅普诺夫稳定性理论,本文建立了一类不确定时滞系统模型,并且得到非线性保性能控制器存在的充分条件,该条件可表示为线性矩阵不等式(LMI)的形式。本文设计的控制器在保证闭环系统的平衡点局部渐近稳定的同时能够满足给定的性能指标,解决了此类时滞系统的非线性保性能控制问题,还利用Matlab软件的LMI工具箱求得不确定时滞系统的闭环保性能指标最优值。通过仿真实例的实施,本文证实了所提供的方法具有切实可行的效果。The problem of nonlinear guaranteed performance control is studied for a class of uncertain time-delay systems.On the basis of the Lyapunov stability theory,a model for uncertain time-delay systems is set up,and thereby the sufficient condition for the existence of the non-linear guaranteed performance controller is obtained,which can be expressed in the form of linear matrix inequality(LMI).The designed controller guarantees local asymptotic stability at the equilibrium of the closed-loop system and satisfies the given performance indicators,thus solving the non-linear guaranteed performance control problem for such time-delay systems.The optimal value of the closed-loop guaranteed performance indicators of the time-delay systems can be obtained by using the LMI toolbox of the Matlab software.A simulation example confirms the feasibility and effectiveness of the proposed method.

关 键 词：非线性保性能控制 不确定时滞系统 LYAPUNOV泛函 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]