连续时间正系统的静态输出反馈鲁棒H∞控制

doi:10.6040/j.issn.1671-9352.0.2015.510

摘要/Abstract

摘要： 利用有界实引理和线性矩阵不等式技术,得到了连续时间正系统静态输出反馈H_∞控制问题可解的一个充要条件。在此基础上给出了连续时间正系统存在静态输出反馈鲁棒H_∞控制器的一个充分条件,所得条件均由带有矩阵等式约束的线性矩阵不等式给出。H_∞控制器增益矩阵可利用锥补线性化技巧来求解。最后,作为静态输出反馈的一种特殊情形,得到了状态反馈控制器存在的一个充分条件,并通过数值仿真验证了结论的正确性。

关键词: 线性矩阵不等式, 静态输出反馈, 锥补线性化, 鲁棒H无穷控制, 正系统

Abstract: A necessary and sufficient condition of static output feedback H_∞ control for continuous-time positive systems was obtained via bounded real lemma and linear matrix inequality. Based on the above condition, a sufficient condition of static output feedback robust H_∞ control for continuous-time positive systems was given. The conditions were established in terms of linear matrix inequalities and a matrix equality constraint. Furthermore, the desired H_∞ controller gain matrix could be determined via cone complementarity linearization techniques. Final, a state controller asspecial case of static output feedback ones was given and a numerical example was provided to illustrate the validity of the results.

Key words: positive systems, static output feedback, cone complementarity linearization, linear matrix inequality, robust H_∞ control

中图分类号:

TP273

徐言超. 连续时间正系统的静态输出反馈鲁棒H_∞控制[J]. 山东大学学报（理学版）, 2016, 51(12): 87-94.

XU Yan-chao. Static output feedback robust H_∞ control for continuous-time positive systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 87-94.

参考文献

[1] BERMAN A, PLEMMONS R J. Nonnegative matrices in the mathematical sciences[M]. Philadelphia, PA: SIAM, 1994.
[2] DE SANTIS A, FARINA L. Identification of positive linear systems with Poisson output transformation[J]. Automatica, 2002, 38(5):861-868.
[3] FARINA L, RINALDI S. Positive linear systems: theory and its applications[M]. New York: Wiley, 2000.
[4] GURVITS L, SHORTEN R, MASON O. On the stability of switched positive linear systems[J]. IEEE Transactions on Automatic Control, 2007, 52(6):1099-1103.
[5] BENVENUTI L, FARINA L. A tutorial on the positive realization problem[J]. IEEE Transactions on Automatic Control, 2004, 49(5):651-664.
[6] NGOC P. Strong stability radii of positive linear time-delay systems[J]. International Journal of Robust and Nonlinear Control, 2005, 15(10):459-472.
[7] BACK J, ASTOLFI A. Design of positive linear observers for positive linear systems via coordinate transformations and positive realizations[J]. SIAM Journal on Control and Optimization, 2008, 47(1):345-373.
[8] 宋世君,冯俊娥,孟敏.受控正系统的弹性静态输出反馈鲁棒H_∞控制[J].控制理论与应用,2014,31(5):671-676. SONG Shijun, FENG June, MENG Min.Robust resilient static output feedback H_∞ control for positive systems[J]. Control Theory & Applications, 2014, 31(5):671-676.
[9] FENG J, LAM J, SHU Z, et al. Internal positivity preserved model reduction[J]. International Journal of Control, 2010, 83(3):574-585.
[10] CHEN X, LAM J, LAM H. Positive filtering for positive Takagi-Sugeno fuzzy systems under l₁ performance[J]. Information Sciences, 2015, 299(1):32-41.
[11] SHEN J, LAM J. l_∞/L_∞-gain analysis for positive linear systems with unbounded time-varying delays[J]. IEEE Transactions on Automatic Control, 2015, 60(3):857-862.
[12] 李振波,朱淑倩. 受控正时滞系统的弹性静态输出反馈镇定[J]. 山东大学学报(工学版),2011,41(3):46-52. LI Zhenbo, ZHU Shuqian. Resilient static output feedback stabilization for controlled positive time-delay systems[J]. Journal of Shandong University(Engineering Science), 2011, 41(3):46-52.
[13] MASON O, SHORTEN R. On linear copositiveLyapunov functions and the stability of switched positive linear systems[J]. IEEE Transactions on Automatic Control, 2007, 52(7):1346-1349.
[14] RAMI M A. Solvability of static output-feedback stabilization for LTI positive systems[J]. Systems & Control Letters, 2011, 60(9):704-708.
[15] YOSHIDA H, TANAKA T. Positive controllability test for continuous-time linear systems[J]. IEEE Transactions on Automatic Control, 2007, 52(9):1685-1689.
[16] FENG J, LAM J, LI P, et al. Decay rate constrained stabilization of positive systems using static output feedback[J]. International Journal of Robust and Nonlinear Control, 2011, 21(1):44-54.
[17] LIAN J, LIU J, ZHUANG Y. Mean stability of positive Markov jump linear systems with homogeneous and switching transition probabilities[J]. IEEE Transactions on Circuits Systems II, 2015, 62(8):801-805.
[18] ZHU S, HAN Q, ZHANG C. Investigating the effects of time-delays on stochastic stability and designing l₁-gain controllers for positive discrete-time Markov jump linear systems with time-delay[J]. Information Sciences, 2016, 355(10):265-281.
[19] GAHINET P, APKARIAN P. A linear matrix inequality approach to H_∞ control[J]. International Journal of Robust and Nonlinear Control, 1994, 4:421-448.
[20] 张卫, 鞠培军.广义变时滞区间系统的鲁棒H_∞弹性控制[J]. 山东大学学报(理学版),2008,43(4):58-61. ZHANG Wei, JU Peijun. Robust resilient H_∞ control for interval singular systems with time-varying delays[J]. Journal of Shandong University(Nature Science), 2008, 43(4):58-61.
[21] 孙林, 郑煜, 姚娟. 不确定离散奇异系统的鲁棒非脆弱H_∞状态反馈控制[J].山东大学学报(理学版),2011, 46(1):35-41. SUN Lin, ZHENG Yu, YAO Juan. Robust non-fragile H_∞ state feedback control for uncertainty discrete singular systems[J]. Journal of Shandong University(Nature Science), 2011, 46(1):35-41.
[22] YANG Guanghong, WANG Jianliang. Non-fragile H_∞ control for linear systems with multiplicative controller gain variations[J]. Automatica, 2001, 37(5):727-737.
[23] 鲁仁全, 苏宏业,薛安克, 等. 奇异系统的鲁棒控制理论[M]. 北京:科学出版社,2008.
[24] LI P, LAM J, SHU Z. H_∞ positive filtering for positive linear discrete-time systems: an augmentation approach[J]. IEEE Transactions on Automatic Control, 2010, 55(10):2337-2342.
[25] TANAKA T, LANGBORT C. The bounded real lemma for internally positive systems and H_∞ structured static state feedback[J]. IEEE Transactions on Automatic Control, 2011, 56(9):2218-2223.
[26] EI GHAOUI L, OUSTRY F, AITRAMI M. A cone complementarity linearization algorithm for static output-feedback and related problems[J]. IEEE Transactions on Automatic Control, 1997, 42(8):1171-1176.

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