一种含扰动离散非线性系统状态观测器的设计方法  

A Design Method of State Observer for Discrete Nonlinear Systems With Disturbances

作　　者：孙延修[1] 黎虹[1] 龙佳 SUN Yanxiu;LI Hong;LONG Jia(Basic Course Department,Shenyang Institute of Technology,Fushun 113122,China)

机构地区：[1]沈阳工学院基础课部,辽宁抚顺113122

出　　处：《沈阳大学学报（自然科学版）》2024年第4期306-311,共6页Journal of Shenyang University：Natural Science

基　　金：2022年辽宁省教育厅基本科研项目(JYT2022MSL04);2023年辽宁省科技厅应用基础研究计划项目(2023JH2/101300220)。

摘　　要：针对一类含扰动的非线性离散系统,讨论了系统状态观测器的设计问题,给出了一种离散系统状态观测器的设计方法,并将该方法应用到奇异系统观测器设计中。首先,根据李雅普诺夫稳定性理论,得到离散系统在不含外部扰动下观测器增益矩阵存在的充分条件;其次,考虑到离散系统的扰动项,针对系统中的外部扰动在李雅普诺夫函数设计中纳入性能指标,得到含扰动情况下离散系统观测器增益矩阵存在的充分条件,该方法可以通过设置性能指标减弱扰动对系统状态估计的影响,同时也有利于增益矩阵的设计与求解;最后,将非线性离散系统观测器的设计方法推广到奇异系统中,从而使该方法更具一般性。利用三个数值算例对所提方法进行了检验,仿真结果表明了文中所提方法的可行性与有效性。The design of state observer for a class of nonlinear discrete systems with disturbances was discussed.Firstly,based on Lyapunov stability theory,a sufficient condition for the existence of the observer gain matrix in discrete systems without external disturbances was obtained.Secondly,considering the disturbance term of the discrete system,performance indicators were incorporated into the Lyapunov function design for external disturbances in the system.A sufficient condition for the existence of the observer gain matrix of the discrete system with disturbances was obtained.This method could weaken the influence of disturbances on system state estimation by setting performance indicators,and was also conducive to the design and solution of gain matrix.Finally,the design method of nonlinear discrete system observers was extended to singular systems,making the method more general.Three numerical examples were used to validate the proposed method,and the simulation results showed the feasibility and effectiveness of the proposed method.

关 键 词：非线性系统 离散系统 观测器 线性矩阵不等式 增益矩阵 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]