孙延修;黎虹;潘斌;

• 1:沈阳工学院基础课部
• 2:辽宁石油化工大学理学院

摘要(Abstract)：

针对一类满足Lipschitz条件的非线性时滞广义系统,讨论了系统观测器的设计问题.首先,通过对时滞广义系统的线性变换,将系统转化为易于求取观测器的形式;其次,将系统分两种情况分别设计出了相应的观测器,通过构造Lyapunov函数利用Schur补引理给出了观测器存在的充分条件;最后,给出一个数值算例,通过利用线性矩阵不等式(LMI)求解出了非线性时滞广义系统观测器的增益矩阵,验证了观测器设计方法的可行性.

关键词(KeyWords)： 观测器;非线性广义系统;时滞;Lyapunov函数

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(61602228,61572290)

作者(Authors): 孙延修;黎虹;潘斌;

参考文献(References)：

• [1] Zhu F L, Han Z Z. A note on observers for Lipschitz nonlinear systems[J]. IEEE Transactions on Automatic Control, 2002,47(10):1751-1754.
• [2] Chen W T, Saif M. Unknown input observer design for a class of nonlinear systems:an LMI approach:proceedings of the 2006 American Control Conference, Minneapolis[C]. Piscataway:IEEE Press, 2006:834-838.
• [3] Zhu F L, Cen F. Full-order observer-based actuator fault detection and reduced-order observerbased fault reconstruction for a class of uncertain nonlinear systems[J]. Journal of Process Control,2010,20(10):1141-1149.
• [4]范子荣,滕青芳.一类非线性系统的观测器设计[J].计算机仿真, 2014,31(1):403-406.
• [5] Xu S, Lu J, Zhou S, et al. Design of observers for a class of discrete-time uncertain nonlinear systems with time delay[J]. Journal of the Franklin Institute, 2004,341(3):295-308.
• [6] Trinh H, Aldeen M, Nahavandi S. An observer design procedure for a class of nonlinear time-delay systems[J]. Computers&Electrical Engineering, 2004,30(1):61-71.
• [7] Raff T, Allgwer F. An EKF-based observer for nonlinear time-delay systems:American Control Conference ACC′06, Minneapolis[C]. New York:Springer-Verlag, 2006:1676-1681.
• [8] Zemouche A, Boutayeb M. A new observer design method for a class of Lipschitz nonlinear discretetime systems with time-delay extension to performance analysis:the 46th IEEE Conference on Decision and Control. New Orleans[C]. New York:Springer-Verlag, 2007:414-419.
• [9] Lu G P. Robust observer design for Lipschitz nonlinear discrete-time systems with time-delay:9th International Conference on Control, Automation, Robotics and Vision. Singapore[C]. New York:Springer-Verlag, 2006:1-5.
• [10]杨洪金,井元伟,肇和平.非线性系统观测器的设计:LMI方法[J].信息与控制, 2011,40(4):433-437.
• [11]张悦,杨洪金,肇和平,等.时滞Lipschitz非线性系统观测器设计[J].东北大学学报(自然科学版),2011,32(11):1521-1524.
• [12]郭真真,高存臣.一类时滞离散非线性系统的全维观测器设计[J].南京信息工程大学学报(自然科学版), 2016,8(1):91-96.
• [13] Gao Zhiwei, Ho D W C. State/noise estimator for descriptor systems with application to sensor fault diagnosis[J]. IEEE Trans. on Signal Processing, 2006,54(4):1316-1326.
• [14] Yang Junqi, Zhu Fanglai. Robust sliding mode observer based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems[J]. International Journal of Control Automation and Systems, 2015,13(5):1037-1046.
• [15] Yu Jingyong, Liu Zhiyuan. Fault reconstruction based on sliding mode observer for linear descriptor systems:proceeding of the 7th Asian Control Conference, Hong Kong[C]. Piscataway:IEEE Press,2009:1132-1137.
• [16]孙延修.一类基于离散广义时滞系统观测器的存在性判据[J].沈阳大学学报(自然科学版),2018,30(4):299-301.
• [17] Tang Hongji, Han Yanwu. Full-order and reduced-order observer for a class of Lipschitz descriptor systems with delay[J]. Journal of Natural Science of Hei Longjiang University, 2012,29(5):593-601.
• [18]孙延修,黎虹,潘斌.一类时滞Lipschitz非线性离散广义系统观测器的设计[J].纯粹数学与应用数学,2018,34(3):316-322.