不确定中立型变时滞系统基于状态观测器的滑模控制
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摘要
本文讨论了不确定中立型变时滞系统的滑模控制问题。首先,为了估计所要研究的不确定中立型系统的状态,构造了一个状态观测器,并设计了滑模控制律,以保证切换面的有限时间可达性。其次,基于Laypunov-Krasovskii泛函法以及线性矩阵不等式(LMI)等方法,给出了误差系统和滑模动力方程的渐近稳定性判据。最后,给出了一个数值算例说明了文本结果的有效性和可行性。
This paper is concerned with sliding mode control for uncertain neutral type systems with time-varying delays. Firstly, a observer is constructed to estimate the state of neutral type systems of the study, a switching function is defined based on the new observer and a sliding mode control law is designed to guarantee the reach-ability of the switching surface in a finite time interval. Secondly, based on the Laypunov-Krasovskii functional method, sufficient condition on asymptotic stability of the error system and sliding mode dynamics equation are presented in terms of linear matrix inequalities(LMI). Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed results.
This paper is concerned with sliding mode control for uncertain neutral type systems with time-varying delays. Firstly, a observer is constructed to estimate the state of neutral type systems of the study, a switching function is defined based on the new observer and a sliding mode control law is designed to guarantee the reach-ability of the switching surface in a finite time interval. Secondly, based on the Laypunov-Krasovskii functional method, sufficient condition on asymptotic stability of the error system and sliding mode dynamics equation are presented in terms of linear matrix inequalities(LMI). Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed results.
引文
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[13] Xiang Zhengrong,Sun Yanan,Chen Qingwei.Robust reliable stabilization of uncertain switched neutral systems with delayed switching[J].Appl Math Comput,2011,217(23):9835-9844.
[14] Bout M,Darouach M.A reduced-order observer for nonlinear discrete time systems[J].System and Control Letters,2000,39(2):141-151.
[15] Dong Yali,Mei Shengwei.State observers for a class of multi-output nonlinear dynamic systems[J].Nonlinear Analysis,2011,74(14):4738-4745.
[16] Zhang Wei,Su Housheng,Wang Hongwei,et al.Full-order and reduced-order observers for one-side Lipschitz nonlinear systems using Riccati equations[J].Commun Nonlinear Sci Numer Simulat,2012,17(12) :4968-4977.
[17] Zhang P,Kao Y G,Zhu J Y,et al.H∞ Observer-based sliding mode control for uncertain stochastic systems with time-varying delay[J].Mathematical Problems in Engineering,2013(6):1-8.
[2] 吴敏,何勇.时滞系统鲁棒控制:自由权矩阵方法[M].北京:科学出版社,2008.Wu Min,He Yong.Robust Control with Time-Varying Delay System:Free-Weighting Matrices Method[M].Beijing:Science Press,2008.
[3] 廖晓欣.稳定性的理论和应用[M].武汉:华中师范大学出版社,1998.Liao Xiaoxin.Stability of Mathematical Theory and Application[M].Wuhan:East China Normal University Press,1998.
[4] 高为炳.变结构控制理论及设计方法[M].北京:科学出版社,1996.Gao Weibing.Variable Structure Control Theory and Design Method[M].Beijing:Science Press,1996.
[5] 高存臣,袁付顺,肖会敏.时滞变结构控制系统[M].北京:科学出版社,2004.Gao Cunchen,Yuan Fushun,Xiao Huimin.Variable Structure Control System with Time-varying Delay[M].Beijing:Science Press,1996.
[6] Liu Pin-Lin,Su Te-Jen.Robust stability of interval time-delay systems with delay-dependence[J].Systems & Control Letters,1998,33(4):231-239.
[7] Wang Cheng,Shen Yi.Improved delay-dependent robust stability criteria for uncertain time delay systems[J].Applied Mathematics and Computation,2011,218(6):2880-2888.
[8] He Y,Wu M,She J H,et al.Delay-dependent robust stability criteria for uncertain neutral type systems with mixed delays[J].Syst Control Lett,2004,51(1):57-65.
[9] Han Q L.Robust stability of uncertain delay-differential systems of neutral type[J].Automatica,2002,38(4):719-723.
[10] Park J H.LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients[J].Elsevier Science Inc,2005,160(2):355-361.
[11] Yang M S,Liu P L.On asymptotic stability of linear neutral delay differential systems[J].Internat J Syst Sci,2002,33(11):901-907.
[12] Li H,Zhong S M,Li H B.Some new simple stability criteria of linear neutral systems with a single delay[J].J Comput Appl Math,2007,200(1):441-447.
[13] Xiang Zhengrong,Sun Yanan,Chen Qingwei.Robust reliable stabilization of uncertain switched neutral systems with delayed switching[J].Appl Math Comput,2011,217(23):9835-9844.
[14] Bout M,Darouach M.A reduced-order observer for nonlinear discrete time systems[J].System and Control Letters,2000,39(2):141-151.
[15] Dong Yali,Mei Shengwei.State observers for a class of multi-output nonlinear dynamic systems[J].Nonlinear Analysis,2011,74(14):4738-4745.
[16] Zhang Wei,Su Housheng,Wang Hongwei,et al.Full-order and reduced-order observers for one-side Lipschitz nonlinear systems using Riccati equations[J].Commun Nonlinear Sci Numer Simulat,2012,17(12) :4968-4977.
[17] Zhang P,Kao Y G,Zhu J Y,et al.H∞ Observer-based sliding mode control for uncertain stochastic systems with time-varying delay[J].Mathematical Problems in Engineering,2013(6):1-8.