Lipschitz非线性离散系统基于观测器的鲁棒镇定控制设计  

Observer-based Robust Stabilization Control Design for Lipschitz Nonlinear Discrete-time Systems

作　　者：鲁润翰 于晓 LU Runhan;YU Xiao(School of Science,Shandong Jianzhu University,Jinan 250000,China)

机构地区：[1]山东建筑大学理学院,山东济南250000

出　　处：《应用数学》2024年第3期779-791,共13页Mathematica Applicata

基　　金：国家自然科学基金(62303280);山东省自然科学基金(ZR2020QA036,ZR2021MF009,ZR2023MF055);湖北省自然科学基金(2022CFB139);山东省高校青创科技计划(2021KJ067);山东建筑大学博研基金(X19053Z)。

摘　　要：本文研究Lipschitz非线性离散时间系统的基于观测器的鲁棒镇定控制问题.首先,针对Lipschitz非线性离散系统,应用微分中值定理和线性参变系统理论,以线性矩阵不等式(LMI)的形式给出基于观测器的鲁棒镇定控制设计的充分条件.随后,将设计结果进一步推广,针对含干扰的Lipschitz非线性离散系统进行H∞性能分析,实现了基于观测器的鲁棒H∞镇定控制,同时给出观测器增益矩阵和控制器增益矩阵的一步求解算法.最后,通过两个数值例子验证了所提方法的有效性.This paper investigates the observer-based robust stabilization control problem for Lipschitz nonlinear discrete-time systems.Firstly,for Lipschitz nonlinear discrete-time systems,a sufficient condition for observer-based robust stabilization control design is given in the form of linear matrix inequality(LMI)by applying the differential mean value theorem and linear parameter-varying system theory.Subsequently,the design result is further generalized and H∞performance analysis is conducted for Lipschitz nonlinear discrete-time systems with disturbances.Observer-based robust H∞stabilization control is achieved,and a one-step algorithm for solving the observer gain matrix and controller gain matrix is provided.Finally,two numerical examples verify the effectiveness of the proposed method.

关 键 词：LIPSCHITZ非线性系统 观测器 输出反馈 鲁棒H∞控制 

分 类 号：O231[理学—运筹学与控制论]