一类Lipschitz非线性时滞离散广义系统降维观测器的设计
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摘要
针对时滞离散广义系统降维观测器的设计问题,提出一类Lipschitz非线性时滞离散广义系统降维观测器的设计方法。首先,基于时滞离散广义系统的可观性对系统进行变换,将系统变换为易于求取降维观测器的形式;其次,基于非线性系统观测器设计的Lyapunov稳定性理论,通过讨论时滞系统中的Lipschitz非线性项,分两种情况设计出了时滞系统的两个降维观测器;最后,为使得时滞系统与降维观测器的误差系统渐近稳定,利用线性矩阵不等式(LMI)的方法分别给出了两个降维观测器存在的充分条件,并通过数值算例验证了该类降维观测器设计方法的有效性。
The design of reduced order observers for discrete time singular systems with time-delay are studied, a design method of observer for a class of nonlinear systems is presented.Firstly, the system is transformed based on the observability of time-delay discrete generalized system, and the system is transformed into the form of reduced dimensional observer; Secondly, two reduced-order observer for time-delay system are designed by discussing the nonlinear term of Lipschitz in time-delay system based on the Lyapunov stability theory of nonlinear system observer design; Finally, in order to make the error system of the delay system and the reduced dimensional observer asymptotically stable, the sufficient conditions for the existence of two reduced dimensional observers are given by using the linear matrix inequality(LMI) method, and the numerical example is given to verify the validity of the design method of this kind of observer.
The design of reduced order observers for discrete time singular systems with time-delay are studied, a design method of observer for a class of nonlinear systems is presented.Firstly, the system is transformed based on the observability of time-delay discrete generalized system, and the system is transformed into the form of reduced dimensional observer; Secondly, two reduced-order observer for time-delay system are designed by discussing the nonlinear term of Lipschitz in time-delay system based on the Lyapunov stability theory of nonlinear system observer design; Finally, in order to make the error system of the delay system and the reduced dimensional observer asymptotically stable, the sufficient conditions for the existence of two reduced dimensional observers are given by using the linear matrix inequality(LMI) method, and the numerical example is given to verify the validity of the design method of this kind of observer.
引文
[1] 赵岩斌.一类离散时间非线性系统降维观测器设计[J].数学杂志,2013,33(4):743-751.
[2] 高存臣,李云艳,刘云龙.一类离散非线性系统降维观测器设计[J].中国海洋大学学报,2010,40(4):119-121.
[3] DAWSON D M.On the state observation and output feedback problems for nonlinear uncertain dynamic systems[J].Syst.Control Lett.,1992,18:217-222.
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[7] 迟子孟,周磊,王秋琳,等.关于非线性系统降维观测器设计方法的研究[J].哈尔滨师范大学学报(自然科学学版),2015,31(5):1-3.
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[10] 迟子孟,王秋琳,周磊.一类 Lipschitz 非线性系统降维观测器设计[J].哈尔滨师范大学自然科学学报,2014,30(4):1-3.
[11] 杨洪金,肇和平,井元伟,等.时滞Lipschitz 非线性系统观测器设计[J].信息与控制,2012,41(2):210-213.
[12] 屠园园,王大轶,李文博.基于降维观测器的最优故障诊断算法研究[J].中国空间科学技术,2017,37(6):40-45.
[13] 何涌波,赵菲,蔡昌毅,等.基于降维观测器的Takagi-Sugeno模糊非线性系统的故障诊断[J].信息通信,2017,178(10):3-7.
[14] WANG Z,SHEN Y,ZHANG X,et al.Observer design for discrete-time descriptor systems:An LMI approach[J].Systems & Control Letters,2012,61(6):683-687.
[15] DAROUACH M,BOUTAYEB M.Design of observers for descriptor systems[J].IEEE Trans on Automatic Cont- rol,1995,40(7):1323-1327.
[16] DAROUACH M,BOUTAT-BADDAS L.Observers for a class of nonlinear singular systems[J].IEEE Trans on Au- tomatic Control,2008,53(11):2627-2633.
[2] 高存臣,李云艳,刘云龙.一类离散非线性系统降维观测器设计[J].中国海洋大学学报,2010,40(4):119-121.
[3] DAWSON D M.On the state observation and output feedback problems for nonlinear uncertain dynamic systems[J].Syst.Control Lett.,1992,18:217-222.
[4] BESANCON G,HAMMOURI H.On uniform observation of nonuniformly observable systems[J].Syst.Control Lett.,1996,29:9-19.
[5] RAJAMANI R,CHAO Y M.Existence and design of observers for nonlinear systems:relation to distance to unobservability[J].Int.J.Control,1998,69:717-731.
[6] 徐明跃,胡广大.一类非线性系统降维观测器设计[J].哈尔滨理工大学学报,2010,15(4):58-63.
[7] 迟子孟,周磊,王秋琳,等.关于非线性系统降维观测器设计方法的研究[J].哈尔滨师范大学学报(自然科学学版),2015,31(5):1-3.
[8] 韩冬,朱芳来.一类未知输入系统的降维观测器设计[J].上海交通大学学报,2012,46(11):1779-17 84.
[9] 李晓艳,蒋威.广义时滞系统的降维观测器设计[J].计算技术与自动化,2009,28(2):6-8.
[10] 迟子孟,王秋琳,周磊.一类 Lipschitz 非线性系统降维观测器设计[J].哈尔滨师范大学自然科学学报,2014,30(4):1-3.
[11] 杨洪金,肇和平,井元伟,等.时滞Lipschitz 非线性系统观测器设计[J].信息与控制,2012,41(2):210-213.
[12] 屠园园,王大轶,李文博.基于降维观测器的最优故障诊断算法研究[J].中国空间科学技术,2017,37(6):40-45.
[13] 何涌波,赵菲,蔡昌毅,等.基于降维观测器的Takagi-Sugeno模糊非线性系统的故障诊断[J].信息通信,2017,178(10):3-7.
[14] WANG Z,SHEN Y,ZHANG X,et al.Observer design for discrete-time descriptor systems:An LMI approach[J].Systems & Control Letters,2012,61(6):683-687.
[15] DAROUACH M,BOUTAYEB M.Design of observers for descriptor systems[J].IEEE Trans on Automatic Cont- rol,1995,40(7):1323-1327.
[16] DAROUACH M,BOUTAT-BADDAS L.Observers for a class of nonlinear singular systems[J].IEEE Trans on Au- tomatic Control,2008,53(11):2627-2633.