非线性扰动离散广义时滞系统的鲁棒H∞控制

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (4): 916-921.

非线性扰动离散广义时滞系统的鲁棒H_∞控制

沃松林¹, 史国栋¹, 邹云²

1. 江苏技术师范学院电气信息工程学院, 江苏, 常州, 213001;
2. 南京理工大学自动化学院, 江苏, 南京, 210094

收稿日期:2008-01-09 修回日期:2008-05-14 出版日期:2009-04-20 发布日期:2010-01-03
作者简介:沃松林(1964- ),男,教授,博士,主要研究方向为广义大系统理论与分散控制.E-mail:wosonglin2000@yahoo.com.cn
基金资助:
国家自然科学基金(60474078);江苏省青蓝工程资助课题

Robust H-infinity control for discrete-time singular systems with time-delay and nonlinear perturbation

WO Song-lin¹, SHI Guo-dong¹, ZOU Yun²

1. School of Electrical and Information Engineering, Jiangsu Teachers Univ. of Technology, Changzhou 213001, China;
2. School of Automation, Nanjing Univ. of Science and Technology, Nanjing 210094, China

Received:2008-01-09 Revised:2008-05-14 Online:2009-04-20 Published:2010-01-03

摘要/Abstract

摘要： 研究了扰动是满足Lipschitz条件的一类非线性离散广义时滞系统的鲁棒H_∞控制和鲁棒H_∞保性能控制问题。目的是设计系统的鲁棒H_∞控制器和鲁棒H_∞保性能控制器。应用线性矩阵不等式方法,分别给出了系统的鲁棒H_∞控制器和鲁棒H_∞保性能控制器存在的充分条件;并在这些条件可解时,分别给出了鲁棒H_∞控制器和鲁棒H_∞保性能控制器的表达式。最后用例子说明了所给方法的应用。

Abstract: This paper discusses the robust H-infinity control problem and robust H-infinity guaranteed cost control problem for discrete-time singular systems with time-delay and nonlinear perturbation,which satisfies Lipschitz condition.The aims are to design a robust H-infinity controller and a robust H-infinity guaranteed cost controller,respectively.By means of the linear matrix inequality approach(LMI),sufficient conditions for existence of robust H-infinity controller and robust H-infinity guaranteed cost controller are presented,respectively.When these LMIs are feasible,the explicit expressions of robust H-infinity controller and robust H-infinity guaranteed cost controller are obtained,respectively.Finally,a numerical example is provided to demonstrate the application of the proposed method.

中图分类号:

TP273

沃松林, 史国栋, 邹云. 非线性扰动离散广义时滞系统的鲁棒H_∞控制[J]. Journal of Systems Engineering and Electronics, 2009, 31(4): 916-921.

WO Song-lin, SHI Guo-dong, ZOU Yun. Robust H-infinity control for discrete-time singular systems with time-delay and nonlinear perturbation[J]. Journal of Systems Engineering and Electronics, 2009, 31(4): 916-921.

参考文献

[1] Chou J H,Liao W H.Stability robustness of continuous-time perturbed descriptor systems[J].IEEE Trans.on Circuits Syst.1,1999,46(9):1153-1155.
[2] Dai L.Singular Control Systems[M].Springe,Verlag,Berlin,1989.
[3] Lin J L,Cben S J.Robust analysis of uncertain linear singular systems with output feedback control[J].IEEE Trans.on Automat.Contr.,1999,44(10):1924-1929.
[4] Masubuchia I,Kamitaneb Y,Oharac A,et al.H_∞ Control for descriptor systems:a matrix inequalities approach[J].Automatica,1997,33(4):669-673.
[5] Xu S Y,Dooren P V,Stefen R,et al.Robust stability and stabilization for singular systems with state delay and parameter uncertainty[J].IEEE Trans.on Automat.Contr.,2002,47(7):1122-1128.
[6] Fang C H,Lee L,Chang F R.Robust control analysis and design for discrete-time singular systems[J].Automatica,1994,30(11):1741-1750.
[7] Xu S Y,Lam J,Yang C W.Quadratic stability and stabilization of uncertain linear discrete-time systems with delay[J].Syst.Contr.Lett.,2001,43(2):77-84.
[8] Xu S Y,Yang C W,Niu Y G,et al.Robust stabilization for uncertain discrete singular systems[J].Automation,2001,37(5):767-774.
[9] Xu S Y,Lam J,Zhang L Q.Robust D-stability analysis for uncertain discrete singular systems with state delay[J].IEEE Trans.on Automatic Control,2002,49(4):551-555.
[10] Xu S Y,Lam J,Yang C W.Robust H_∞ control for discrete singular systems with state delay and parameter uncertainty[J].Dynamics of Continuous,Discrete and Impulsive Systems.Series B:Applications and Algorithms,2002,9(4):539-554.
[11] 沃松林,史国栋,邹云,不确定离散广义线性系统的保性能最优控制[J].系统工程与电子技术,2005,27(1):100-103.(Wo Songlin,Shi Guodung,Zou Yun.Optimal guaranteed cost control for uncertain discrete-time singular linear systems[J].Systems Engineering and Electronics,2005,27(1):100-103.)
[12] Wo Songlin,Shi Guodong,Zou Yun.Guaranteed cost control for discrete-time singular large-scale systems with parameter uncertainty[J].Acta Automatica Sinica,2005,31 (5):808-814.
[13] 冯俊娥,程兆林.不确定奇异时滞系统的保性能控制[J].控制与决策,2002,17(B11).-711-714.
[14] Liu G P,Daniel W C Ho.Generalized quadratic stabilization for discrete-time singular systems with time-delay and nonlinear perturbation[J].Asian Journal of Control,2005,7(3):221-222.
[15] 沃松林,史国栋,邹云.具有非线性扰动的离散奇异时滞系统的保性能控制[J].控制与决策.2007,22(6):670-674.