Finite Frequency H_∞ Filtering for Continuous 2-D Roesser Systems
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- 英文论文题名：Finite Frequency H_∞ Filtering for Continuous 2-D Roesser Systems
- 论文作者：Zhaoxia Duan ; Jian Shen ; Wenyong Duan
- 英文论文作者：Zhaoxia Duan ; Jian Shen ; Wenyong Duan ; College of Energy and Electrical Engineering ; Hohai University ; School of Sciences ; Nanjing University of Science and Technology ; School of Electrical Engineering ; Yancheng Institute of Technology
- 年：2017
- 作者机构：College of Energy and Electrical Engineering,Hohai University;School of Sciences,Nanjing University of Science and Technology;School of Electrical Engineering,Yancheng Institute of Technology;
- 英文论文关键词：finite frequency ; H∞ filtering ; 2-D continuous system
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TN713
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：480k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers the problem of finite frequency(FF) H_∞ filtering for two-dimensional(2-D) continuous systems described by the Roesser state-space. Our attention is focused on designing filters guaranteeing the bounded-input-boundedoutput(BIBO) stability and FF H_∞ disturbance attenuation level of the filtering error system. By the generalized KalmanYakubovich-Popov lemma for 2-D continuous systems, the existence conditions of FF H_∞ filters are obtained in terms of solving liner matrix inequalities(LMIs). An example is given to validate the proposed methods.
This paper considers the problem of finite frequency(FF) H_∞ filtering for two-dimensional(2-D) continuous systems described by the Roesser state-space. Our attention is focused on designing filters guaranteeing the bounded-input-boundedoutput(BIBO) stability and FF H_∞ disturbance attenuation level of the filtering error system. By the generalized KalmanYakubovich-Popov lemma for 2-D continuous systems, the existence conditions of FF H_∞ filters are obtained in terms of solving liner matrix inequalities(LMIs). An example is given to validate the proposed methods.
This paper considers the problem of finite frequency(FF) H_∞ filtering for two-dimensional(2-D) continuous systems described by the Roesser state-space. Our attention is focused on designing filters guaranteeing the bounded-input-boundedoutput(BIBO) stability and FF H_∞ disturbance attenuation level of the filtering error system. By the generalized KalmanYakubovich-Popov lemma for 2-D continuous systems, the existence conditions of FF H_∞ filters are obtained in terms of solving liner matrix inequalities(LMIs). An example is given to validate the proposed methods.
引文
[1]Barry P,Gran R,Waters C.Two dimensional filtering-A state estimator approach.In 1976 IEEE conference decision control,1-3 December 1976,15,pp.613-618.
[2]Kaczorek T.Two-dimensional linear systems.Berlin:SpringerVerlag,1985.
[3]Lu W,Antoniou A.Two-dimensional digital filters.New York:Marcel Dekker,1992.
[4]Galkowski K,Rogers E,Paszke W,Owens D.Linear repetitive process control theory applied to a physical example.International Journal of Applied Mathematics and Computer Science,2003,13(1),87-99.
[5]Lam J,Xu S,Zou Y,et al.Robust output feedback stabilization for two-dimensional continuous systems in Roesser form.Applied Mathematics Letters,2004,17(12),1331-1341.
[6]Roesser R.A discrete state-space model for linear image processing.IEEE Transactions on Automatic Control,1975,20(1),1-10.
[7]Fornasini E,Marchesini G.Doubly-indexed dynamical systems:State-space models and structural properties.Mathematical Systems Theory,1978,12(1),59-72.
[8]Wang Z,Liu X.Robust stability of two-dimensional uncertain discrete systems.Signal Processing Letters,IEEE,2003,10(5),133-136.
[9]Hinamoto T.2-D Lyapunov equations and filter design based on the Fornasini-Marchesini second model.IEEE Transactions on Circuits and Systems I,Fundamental Theory and Application,1993,40(2),102-110.
[10]Lam J,Xu S,Zou Y,Lin Z,Galkowski K.Robust output feedback stabilization for two-dimensional continuous systems in Roesser form.Applied Mathematics Letters,2004,17(12),1331-1341
[11]Lu W,Lee E.Stability analysis for two-dimensional systems via a Lyapunov approach.IEEE Transactions on Circuits Systems,1985,32(1),61-68.
[12]Paszke W,Galkowski K,Rogers E,Owens D.H∞and guaranteed cost control of discrete linear repetitive processes.Linear Algebra and Its Applications,2006,412(2-3),93-131.
[13]Li X,Li Z,Gao H.Further results on H∞filtering for discretetime systems with state delay.International Journal of Robust and Nonlinear Control,2011,21(3),248-270.
[14]Liang J,Sun F,Liu X.Finite-horizon H∞filtering for timevarying delay systems with randomly varying nonlinearities and sensor saturations.Systems Science and Control Engineering,2014,2(1):108-118.
[15]Zhang H,Lun S,Liu D.Fuzzy H∞filter design for a class of nonlinear discrete-time systems with multiple time delays.IEEE Transactions on Fuzzy Systems,2007,15(3):453-469.
[16]Katayama T,Kosaka M.Recursive filtering algorithm for a2-D system.IEEE Transactions on Automatic Control,1979,24(1),130-132.
[17]Woods J,Ingle V.Kalman filtering in two dimensions:further results.IEEE Transactions on Acoustics,Speech and Signal Processing,1981,29(2),188-197.
[18]Du C,Xie L.H∞control and filtering of two-dimensional systems.Berlin Heidelberg:Springer-Verlag,2002.
[19]Zhang X,Yang G.Delay-dependent filtering for discrete-time systems with finite frequency small gain specifications.In Proceedings of joint 48th IEEE conference of decision and control&28th Chinese control conference,Shanghai,P.R.China,16-18,Dec.2009,pp.4420-4425.
[20]Tuan H,Apkarian P,Nguyen T.Robust mixed H2/H∞filtering of 2-D systems.IEEE Transactions on Signal Processing,2002,50(7),1759-1771.
[21]Chen S,Fong I.Robust filtering for 2-D state-delayed systems with NFT uncertainties.IEEE Transactions on Signal Processing,2006,54(1),274-285.
[22]Wu L,Lam J,Paszke W,Galkowski K,Rogers E.Robust H∞filtering for uncertain differential linear repetitive processes.International Journal of Adaptive Control and Signal Processing,2008,22(3),243-256.
[23]El-Kasri C,Hmamed A,Tissir E,Tadeo F.Robust H∞filtering for uncertain two-dimensional continuous systems with timevarying delays.Multidimensional Systems and Signal Processing,2013,24(4):685-706.
[24]Xu S,Lam J,Zou Y,et al.Robust H∞filtering for uncertain2-D continuous systems.IEEE Transactions on Signal Processing,2005,53(5):1731-1738.
[25]Chen Y,Zhang W,Gao H.Finite frequency H∞control for building under Earthquake excitation.Mechatronics,2010,20(1),128-142.
[26]Iwasaki T,Hara S.Generalized KYP lemma:Unified frequency domain inequalities with design applications.IEEE Transactions on Automatic Control,2005,50(1),41-59.
[27]Yang R,Xie L,Zhang C.Generalized two-dimensional Kalman-Yakubovich-Popov lemma for discrete Roesser model.IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(10):3223-3233.
[28]Li X,Gao H.Robust finite frequency H∞filtering for uncertain 2-D Roesser systems.Automatica,2012,48(6):1163-1170.
[29]Li X,Gao H,Wang C.Generalized Kalman-YakubovichPopov lemma for 2-D FM LSS model.IEEE Transactions on Automatic Control,2012,57(12):3090-3103.
[30]Bachelier O,Mehdi D.On the KYP lemma,the hybrid Roesser models and the matrix D-regularity.LAII-ESIP Research Report No.20060916OB,2006.
[31]Duan Z,Xiang Z.Finite frequency H∞control of 2-D continuous systems in Roesser model.Multidimensional Systems&Signal Processing,2016,doi:10.1007/s11045-016-0430-3.
[32]Gahinet P,Apkarian P.A linear matrix inequality approach to H∞control.International journal of robust and nonlinear control,1994,4(4),421-448.
[33]Xu S,Lam J,Zou Y,Lin Z,Galkowski K.H∞output feedback control for two-dimensional continuous systems.Dynamics of Continuous Discrete and Impulsive Systems,2008,1(1),1-14.
[2]Kaczorek T.Two-dimensional linear systems.Berlin:SpringerVerlag,1985.
[3]Lu W,Antoniou A.Two-dimensional digital filters.New York:Marcel Dekker,1992.
[4]Galkowski K,Rogers E,Paszke W,Owens D.Linear repetitive process control theory applied to a physical example.International Journal of Applied Mathematics and Computer Science,2003,13(1),87-99.
[5]Lam J,Xu S,Zou Y,et al.Robust output feedback stabilization for two-dimensional continuous systems in Roesser form.Applied Mathematics Letters,2004,17(12),1331-1341.
[6]Roesser R.A discrete state-space model for linear image processing.IEEE Transactions on Automatic Control,1975,20(1),1-10.
[7]Fornasini E,Marchesini G.Doubly-indexed dynamical systems:State-space models and structural properties.Mathematical Systems Theory,1978,12(1),59-72.
[8]Wang Z,Liu X.Robust stability of two-dimensional uncertain discrete systems.Signal Processing Letters,IEEE,2003,10(5),133-136.
[9]Hinamoto T.2-D Lyapunov equations and filter design based on the Fornasini-Marchesini second model.IEEE Transactions on Circuits and Systems I,Fundamental Theory and Application,1993,40(2),102-110.
[10]Lam J,Xu S,Zou Y,Lin Z,Galkowski K.Robust output feedback stabilization for two-dimensional continuous systems in Roesser form.Applied Mathematics Letters,2004,17(12),1331-1341
[11]Lu W,Lee E.Stability analysis for two-dimensional systems via a Lyapunov approach.IEEE Transactions on Circuits Systems,1985,32(1),61-68.
[12]Paszke W,Galkowski K,Rogers E,Owens D.H∞and guaranteed cost control of discrete linear repetitive processes.Linear Algebra and Its Applications,2006,412(2-3),93-131.
[13]Li X,Li Z,Gao H.Further results on H∞filtering for discretetime systems with state delay.International Journal of Robust and Nonlinear Control,2011,21(3),248-270.
[14]Liang J,Sun F,Liu X.Finite-horizon H∞filtering for timevarying delay systems with randomly varying nonlinearities and sensor saturations.Systems Science and Control Engineering,2014,2(1):108-118.
[15]Zhang H,Lun S,Liu D.Fuzzy H∞filter design for a class of nonlinear discrete-time systems with multiple time delays.IEEE Transactions on Fuzzy Systems,2007,15(3):453-469.
[16]Katayama T,Kosaka M.Recursive filtering algorithm for a2-D system.IEEE Transactions on Automatic Control,1979,24(1),130-132.
[17]Woods J,Ingle V.Kalman filtering in two dimensions:further results.IEEE Transactions on Acoustics,Speech and Signal Processing,1981,29(2),188-197.
[18]Du C,Xie L.H∞control and filtering of two-dimensional systems.Berlin Heidelberg:Springer-Verlag,2002.
[19]Zhang X,Yang G.Delay-dependent filtering for discrete-time systems with finite frequency small gain specifications.In Proceedings of joint 48th IEEE conference of decision and control&28th Chinese control conference,Shanghai,P.R.China,16-18,Dec.2009,pp.4420-4425.
[20]Tuan H,Apkarian P,Nguyen T.Robust mixed H2/H∞filtering of 2-D systems.IEEE Transactions on Signal Processing,2002,50(7),1759-1771.
[21]Chen S,Fong I.Robust filtering for 2-D state-delayed systems with NFT uncertainties.IEEE Transactions on Signal Processing,2006,54(1),274-285.
[22]Wu L,Lam J,Paszke W,Galkowski K,Rogers E.Robust H∞filtering for uncertain differential linear repetitive processes.International Journal of Adaptive Control and Signal Processing,2008,22(3),243-256.
[23]El-Kasri C,Hmamed A,Tissir E,Tadeo F.Robust H∞filtering for uncertain two-dimensional continuous systems with timevarying delays.Multidimensional Systems and Signal Processing,2013,24(4):685-706.
[24]Xu S,Lam J,Zou Y,et al.Robust H∞filtering for uncertain2-D continuous systems.IEEE Transactions on Signal Processing,2005,53(5):1731-1738.
[25]Chen Y,Zhang W,Gao H.Finite frequency H∞control for building under Earthquake excitation.Mechatronics,2010,20(1),128-142.
[26]Iwasaki T,Hara S.Generalized KYP lemma:Unified frequency domain inequalities with design applications.IEEE Transactions on Automatic Control,2005,50(1),41-59.
[27]Yang R,Xie L,Zhang C.Generalized two-dimensional Kalman-Yakubovich-Popov lemma for discrete Roesser model.IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(10):3223-3233.
[28]Li X,Gao H.Robust finite frequency H∞filtering for uncertain 2-D Roesser systems.Automatica,2012,48(6):1163-1170.
[29]Li X,Gao H,Wang C.Generalized Kalman-YakubovichPopov lemma for 2-D FM LSS model.IEEE Transactions on Automatic Control,2012,57(12):3090-3103.
[30]Bachelier O,Mehdi D.On the KYP lemma,the hybrid Roesser models and the matrix D-regularity.LAII-ESIP Research Report No.20060916OB,2006.
[31]Duan Z,Xiang Z.Finite frequency H∞control of 2-D continuous systems in Roesser model.Multidimensional Systems&Signal Processing,2016,doi:10.1007/s11045-016-0430-3.
[32]Gahinet P,Apkarian P.A linear matrix inequality approach to H∞control.International journal of robust and nonlinear control,1994,4(4),421-448.
[33]Xu S,Lam J,Zou Y,Lin Z,Galkowski K.H∞output feedback control for two-dimensional continuous systems.Dynamics of Continuous Discrete and Impulsive Systems,2008,1(1),1-14.