船舶运动鲁棒H_∞估计与预报研究
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摘要
船舶在海浪中航行时,在波浪扰动力和力矩的作用下必然会产生六自由度的摇摆运动。如果能够对船舶摇摆状态进行估计和预报,将对舰载机起降、船舶减摇、船舶对接等都具有重要意义。因此,船舶运动估计与预报一直是备受关注的课题。本论文结合国防基金预研项目“航母运动极短期预报及舰载机着舰引导姿态预报系统”和“水面舰船姿态预报控制及仿真研究”,基于鲁棒H∞滤波及奇异系统理论对船舶运动估计和预报问题进行研究。论文的研究内容如下：
论文基于切片理论,运用流体力学知识对船舶运动模型中水动力系数进行了分析,并对水动力系数进行海浪谱加权处理,建立了基于海浪谱加权平均的船舶运动模型,为船舶运动估计与预报的研究提供了标称模型。在船舶运动水动力系数摄动情况下,通过对卡尔曼滤波误差的分析,论证了采用鲁棒H∞方法研究船舶运动估计和预报的必要性。
论文提出了鲁棒H∞估计与预报方法,即综合考虑模型摄动和干扰统计特性未知的因素,针对船舶运动模型摄动设计稳定的滤波器与预报器,并使海浪干扰到船舶运动状态的估计误差和预报误差的衰减水平(H∞范数)小于给定值。主要包括以下三个方面的工作：
1.对于船舶运动估计,利用线性矩阵不等式(LMI)方法,设计了基于二次稳定的船舶运动鲁棒H∞滤波器和基于参数依赖Lyapunov函数的船舶运动鲁棒H∞滤波器,并得到了滤波器的稳定条件及其参数矩阵的求解方法。二次稳定意义下的滤波器设计不需考虑系统参数摄动和干扰的具体性状,设计方法简单易行。但该方法要求对于所有允许的不确定参数存在统一的Lyapunov函数,导致具有较大的保守性。基于参数依赖的鲁棒H∞滤波器,是通过设计与系统的不确定性相关联的Lyapunov函数得到的,减少了设计的保守性,提高了船舶运动估计的精度。
2.船舶运动系统存在奇异摄动现象,论文提出了基于奇异系统的鲁棒H∞估计器的设计方法,并给出了估计器存在的条件,即误差系统是正则、无脉冲和稳定的,利用LMI方法对参数矩阵进行求解。将该方法应用于船舶运动估计,对基于奇异系统理论的船舶运动估计问题进行了仿真研究,验证了该方法的有效性。
3.对于船舶运动预报,提出了船舶运动鲁棒H∞预报器的设计方法,给出了预报器的稳定条件及其参数矩阵的求解过程。将鲁棒H∞预报问题转化为时滞系统的鲁棒H∞滤波问题,并根据时滞依赖和时滞独立的思想,分别设计了预报长度无关型和预报长度相关型鲁棒H∞预报器,利用LMI的线性目标函数最小化方法完成了H∞预报器的求解。该方法解决了模型摄动和海浪干扰统计特性未知时的船舶运动预报问题。
Sailing in the ocean, ship inevitably produces 6-DOF swinging motion under wave disturbing force and disturbance torque. If the ship motion attitude can be estimated and predicted, it will bring great benefit to the take-off and landing of carrier aircraft, ship anti-rolling, ship mating and so on. Therefore, ship motion estimation and prediction have been attracting much attention. Supported by the National Defence Foundation "Extreme Short-time Prediction of Aircraft Carrier and Attitude Prediction System of Guiding Carrier Aircraft Landing" and "Research of Warship Attitude Prediction Control and Simulation", Problem of ship motion estimation and prediction is researched based on robust H∞method in this dissertation. The main contents of this dissertation are as follows:
In this dissertation, the hydrodynamic force coefficients of the ship motion model is analyzed using the hydrodynamics knowledge based on the strip theory. The coefficients are weighted average by wave spectrum, and ship motion model based on weighted average by wave spectrum is established, which provides nominal model for the research of ship motion estimation and prediction. Under the circumstance with pertubing hydrodynamic force coefficients, estimation errors of Kalman filtering is analyzed, and the necessity of applying robust H∞method to research ship motion estimation and prediction is demonstrated.
The methods of robust H∞estimation and prediction are proposed in the dissertation, that is, considering synthetically two aspects of perturbation in ship motion model and unknown uncertainty of disturbance input statistic characteristics, stable filter and predictor is designed to make the attenuation level of wave disturbance to estimation and prediction error (H∞norm) lower than setting value. The main contributions of this dissertation contain the following three aspects:
Firstly, for the ship motion estimation, the ship motion robust H∞filter based on the quadratic stability and parameter-dependent Lyapunov function is designed via linear matrix inequality (LMI) method, and the filter stability condition and the solution method of the parameter matrices are obtained. The filter design based on the quadratic stability does not need to consider material characteristics of parameter perturbations and exogenous disturbance, such that the design method is easily implemented. However, the method requires that there is a unified Lyapunov function for all the permitted uncertain parameters, which leads to more conservativeness. The parameter-dependent robust H∞filter is abtained by designing Lyapunov function correlated with systmen uncertainty, which reduces the design conservativeness and enhances the precision of ship motion estimation.
Secondly, there is singular perturbation phenomenon in ship motion system, thus the robust H∞estimator based on singular system theory and is developed. Existential condition of the estimator that the error system is regular, impulse-free and stabile is given, and its parameter matrices can be derived by resovling linear matrix inequalities. This estimator design method is simulated and applid to the ship motion estimation, simulation result verifies the validity of this method.
Thirdly, ship motion robust H∞predictor is proposed to resolve the problem of ship mition prediction, and stability condition of the predictor and the solution method of parameter matriecs are given. It transforms the problem of robust H∞prediction into the problem of time-delay system robust H∞filtering. The distance-independent and distance-dependent robust H∞predictors are designed according to the delay-independent and delay-dependent ideas, and the solution of H∞, predictor is derived by minimizing linear object functions of LMI. The ship prediction problem with model perturbation and unknown disturbance statistic characteristics can be solved by the proposed method.
论文基于切片理论,运用流体力学知识对船舶运动模型中水动力系数进行了分析,并对水动力系数进行海浪谱加权处理,建立了基于海浪谱加权平均的船舶运动模型,为船舶运动估计与预报的研究提供了标称模型。在船舶运动水动力系数摄动情况下,通过对卡尔曼滤波误差的分析,论证了采用鲁棒H∞方法研究船舶运动估计和预报的必要性。
论文提出了鲁棒H∞估计与预报方法,即综合考虑模型摄动和干扰统计特性未知的因素,针对船舶运动模型摄动设计稳定的滤波器与预报器,并使海浪干扰到船舶运动状态的估计误差和预报误差的衰减水平(H∞范数)小于给定值。主要包括以下三个方面的工作：
1.对于船舶运动估计,利用线性矩阵不等式(LMI)方法,设计了基于二次稳定的船舶运动鲁棒H∞滤波器和基于参数依赖Lyapunov函数的船舶运动鲁棒H∞滤波器,并得到了滤波器的稳定条件及其参数矩阵的求解方法。二次稳定意义下的滤波器设计不需考虑系统参数摄动和干扰的具体性状,设计方法简单易行。但该方法要求对于所有允许的不确定参数存在统一的Lyapunov函数,导致具有较大的保守性。基于参数依赖的鲁棒H∞滤波器,是通过设计与系统的不确定性相关联的Lyapunov函数得到的,减少了设计的保守性,提高了船舶运动估计的精度。
2.船舶运动系统存在奇异摄动现象,论文提出了基于奇异系统的鲁棒H∞估计器的设计方法,并给出了估计器存在的条件,即误差系统是正则、无脉冲和稳定的,利用LMI方法对参数矩阵进行求解。将该方法应用于船舶运动估计,对基于奇异系统理论的船舶运动估计问题进行了仿真研究,验证了该方法的有效性。
3.对于船舶运动预报,提出了船舶运动鲁棒H∞预报器的设计方法,给出了预报器的稳定条件及其参数矩阵的求解过程。将鲁棒H∞预报问题转化为时滞系统的鲁棒H∞滤波问题,并根据时滞依赖和时滞独立的思想,分别设计了预报长度无关型和预报长度相关型鲁棒H∞预报器,利用LMI的线性目标函数最小化方法完成了H∞预报器的求解。该方法解决了模型摄动和海浪干扰统计特性未知时的船舶运动预报问题。
Sailing in the ocean, ship inevitably produces 6-DOF swinging motion under wave disturbing force and disturbance torque. If the ship motion attitude can be estimated and predicted, it will bring great benefit to the take-off and landing of carrier aircraft, ship anti-rolling, ship mating and so on. Therefore, ship motion estimation and prediction have been attracting much attention. Supported by the National Defence Foundation "Extreme Short-time Prediction of Aircraft Carrier and Attitude Prediction System of Guiding Carrier Aircraft Landing" and "Research of Warship Attitude Prediction Control and Simulation", Problem of ship motion estimation and prediction is researched based on robust H∞method in this dissertation. The main contents of this dissertation are as follows:
In this dissertation, the hydrodynamic force coefficients of the ship motion model is analyzed using the hydrodynamics knowledge based on the strip theory. The coefficients are weighted average by wave spectrum, and ship motion model based on weighted average by wave spectrum is established, which provides nominal model for the research of ship motion estimation and prediction. Under the circumstance with pertubing hydrodynamic force coefficients, estimation errors of Kalman filtering is analyzed, and the necessity of applying robust H∞method to research ship motion estimation and prediction is demonstrated.
The methods of robust H∞estimation and prediction are proposed in the dissertation, that is, considering synthetically two aspects of perturbation in ship motion model and unknown uncertainty of disturbance input statistic characteristics, stable filter and predictor is designed to make the attenuation level of wave disturbance to estimation and prediction error (H∞norm) lower than setting value. The main contributions of this dissertation contain the following three aspects:
Firstly, for the ship motion estimation, the ship motion robust H∞filter based on the quadratic stability and parameter-dependent Lyapunov function is designed via linear matrix inequality (LMI) method, and the filter stability condition and the solution method of the parameter matrices are obtained. The filter design based on the quadratic stability does not need to consider material characteristics of parameter perturbations and exogenous disturbance, such that the design method is easily implemented. However, the method requires that there is a unified Lyapunov function for all the permitted uncertain parameters, which leads to more conservativeness. The parameter-dependent robust H∞filter is abtained by designing Lyapunov function correlated with systmen uncertainty, which reduces the design conservativeness and enhances the precision of ship motion estimation.
Secondly, there is singular perturbation phenomenon in ship motion system, thus the robust H∞estimator based on singular system theory and is developed. Existential condition of the estimator that the error system is regular, impulse-free and stabile is given, and its parameter matrices can be derived by resovling linear matrix inequalities. This estimator design method is simulated and applid to the ship motion estimation, simulation result verifies the validity of this method.
Thirdly, ship motion robust H∞predictor is proposed to resolve the problem of ship mition prediction, and stability condition of the predictor and the solution method of parameter matriecs are given. It transforms the problem of robust H∞prediction into the problem of time-delay system robust H∞filtering. The distance-independent and distance-dependent robust H∞predictors are designed according to the delay-independent and delay-dependent ideas, and the solution of H∞, predictor is derived by minimizing linear object functions of LMI. The ship prediction problem with model perturbation and unknown disturbance statistic characteristics can be solved by the proposed method.
引文
[1]Wiiner, N., Extrapolation, Interpolation and Smoothing of Stationary Time Series[J]. John Wiley and Sons, Inc., New York,1949.
[2]Fleek, J.T. Short Time Prediction of the Motion of a Ship in Waves[C]. in Proc.Ist Conf. On Ships and Waves. Couneil on Wave Research and SNAME.1954.
[3]Bates M.R., Book, D. H. and Powell, F.D., Analog Computer Applications in Predictor Design[J]. IRE Trans. On Elec. Com.,1957. Vol.6(3).
[4]Kaplan P., Sargent, T. P., Theoretical Study of the Motions of the an Aircraft Carrier at Sea[R]. Oceanics,Inc.1965. January, No.65-22.
[5]Kaplan P., Sargent, T. P., A Preliminary Study of Prediction Techniques for Aircraft Carrier Motions SRpt[R].ea,Oceanics,Inc.1965.6:5-23.
[6]Kaplan P. A Study of Prediction Techniques for Aircraft Carrier Motions at Sea[C]. in AIAA 6th ASM.1968 Vol.No.68-123.
[7]Kaplan P., Ross, D. Comparative Performance of wave Measuring systems Mounted on ships in Motion at sea[C]. in 4th National Symp. of Marine Science Inst. ISA,Coco Beach,Florida.1968.
[8]Kalman R.E and Bucy, R.S., New Results in Linear Filtering and Prediction Theory[J]. Transactions of ASME, Journal of Basic Engineering Series, 1961.Vol.83D:95-108.
[9]MENAHEM M.SIDAR BRIAN F.DOOLIN, On the Feasibility of Real-Time Prediction of Aircraft Carrier Motiona at Sea[J]. IEEE Transactions on Automatic Control,1983. Vol.AC-28(3):350-356.
[10]Triantafyllou M., Bodson,M. Real Time Predilection of Marine Vessel Motion Using Kalman Filtering Techniques[C]. in Proc. OTC. Houston,Texas.1982 Vol.
[11]Triantafyllou M. Athans M. Real Time Estimation of the Heaving and Pitching Motions of a Ship Using a Kalman Filter[C]. in Proc. Oeeanics 81. Boston MA. Sep.1981.
[12]M. Triantafyllou, Real Time Prediction and Estimation of Ship Motion Using Kalman Filtering Techniques[R]. NASA-CT-169284 1982. No.82-31637.
[13]Triantaryllou M. Athans M., Real Time Estimation of Motions of a Destroyer Using Kalman Filtering Techniques[R]. Laboratory for information and Decision Systems MIT Cambridge. MAY,1983.
[14]Enochson. The Predietion of ShiP Motion at Sea[C]. in CTC.1963.
[15]Dazell J. F., A Nile on short-time Prediction of ship Motions,[J]. Journal of ship Research,1965. Vol.9(2):48-52.
[16]戴仰山,宋竞正,李维扬,快艇在海浪中的运动[J].哈尔滨工程大学学报1981(02).
[17]Yumon I., Real Time Prediction of Ship Response to Ocean Waves Using Time Series Analysis[J]. OCEANS,1981. Vol.13:1082-1089.
[18]Khan A., Bil, C., Marion,K.E., Ship motion prediction for launch and recovery of air vehicles[J]. OCEANS,2005. Vol.32795-2801.
[19]SUN Li-hong SHEN Ji-hong. Prediction of Ship Pitching Based on Support Vector Machines[C]. in International Conference on Computer Engineering and Technology.2009 Vol.1:380-382.
[20]Nicolau V., Aiordachioaie, D., Popa, R. Neural network prediction of the wave influence on the yaw motion of a ship[C]. in IEEE International Joint Conference on Neural Networks.2004 Vol.4:2801-2806.
[21]虞兰生,戴遗山,船舶运动的自适应预报[J].中国造船,1988.Vol.10(2)：83-86.
[22]郜焕秋,谢楠,盛万安,应用人工神经网络理论的船舶运动包络预报方法[J].中国造船,1994(3)：11-20.
[23]郜焕秋,刘楚学.海上实船运动的极短期预报可行性研究[C].in第四届船舶耐波性学术讨论会论文集.中国造船工程学会.1986.
[24]周淑秋,赵希人,舰船航态极短期预报的非线性方法[J].哈尔滨工程大学学报,1996.Vol.17(4)：1-7.
[25]冯铁城,吴善勤,雷振华,浮式海洋平台运动实时预报[J].海洋工程,1991.Vol.9(3)：23-28.
[26]彭秀艳,船舶在线姿态预报及仿真技术研究[D].自动化学院.博士学位论文.2006,哈尔滨：哈尔滨工程大学.
[27]彭秀艳,赵希人,吕淑萍,魏纳新,具有艏前波观测量的大型舰船姿态 运动预报[J].系统仿真学报,2002.Vol.14(6)：809-814.
[28]谢美萍,沈艳,彭秀艳,赵希人,舰船运动的一种改进经典谱估计方法[J].船舶工程,2000(4)：6-8.
[29]谢美萍,赵希人,基于投影寻踪学习的大型船舶运动极短期预报[J].船舶力学,2000.Vol.4(4)：28-32.
[30]沈继红,尚寿亭,赵希人,舰船纵摇运动函数变换型GM(1,1)模型研究[J].哈尔滨工业大学学报,2001(3).
[31]沈继红,赵希人,利用最小二乘法改进GM(2,1)模型[J].哈尔滨工程大学学报,2001(4)：64-66.
[32]谢美萍,赵希人,基于小波网的船舶运动极短期建模预报[J].船舶力学,2002.Vol.6(2)：15-21.
[33]马洁,刘小河,李国斌,韩志刚,大型舰船纵摇运动的多层递阶预报[J].船舶工程,2006.Vol.28(1)：5-8.
[34]李晖,郭晨,金鸿章,基于WT和MGFPE混合模式的船舶横摇运动长期预测[J].哈尔滨工程大学学报2007.Vol.28(6)：611-615.
[35]孙李红,沈继红,基于改进GM(1,1)模型的舰船纵摇运动预报[J].哈尔滨工程大学学报,2009.Vol.30(3)：287-291.
[36]Friedman J.H., Tukey,J. W., A projection pursuit algorithm for exploratory data analysis[J]. IEEE Trans. Computers,1974. Vol.C-23:881-889.
[37]沈继红,灰色系统理论预测方法研究及其在舰船运动预报中的应用[D].自动化学院.博士学位论文.2001,哈尔滨：哈尔滨工程大学.
[38]张汉国,张洪钺,有关鲁棒状态估计的研究评述[J].北京航天航空大学学报,1992(4)：91-97.
[39]邓自立,王建国,非线性系统的自适应推广KALMAN滤波[J].自动化学报,1987.Vol.13(5)：375-379.
[40]张洪才,张友民,贺志斌,一种鲁棒自适应推广Kalman滤波及其在飞行状态估计中的应用[J].信息与控制,1992.Vol.21(6)：343-347.
[41]王司,邓正隆,基于Krein空间的鲁棒Kalman滤波在传递对准中的应用研究[J].中国惯性技术学报,2006.Vol.14(4)：7-11.
[42]Zames G., Feedback and Optimal Sensitivity:Model Reference Transformations Multiplicative Seminorms and Approximant Inverses[J]. IEEE Trans. On Automatic Control,1981. Vol.26:301-320.
[43]Elsayed A, Grimble, M.J., Ho, D. On H∞ filtering in multivariable discrete-time systems[C]. in IEEE International Symposium on Circuits and Systems.1988 Vol.2:1573-1576.
[44]Soura Dasgupta Minyue Fu, Chris Schwarz, Robust Relative Stability of Time-Invariant and Time-Varying Lattice Filters[J]. IEEE Transactions on Signal Processing,1998. Vol.46(8):2088-2100.
[45]U. Shaked N. Berman,H∞ Nonlinear Filtering of Discrete-Time Processes[J]. IEEE Transactions on Signal Processing,1995. Vol.43(9): 2205-2209.
[46]MagdiS.Mahmoud, Discrete-time systems with linear parameter-varying: stability and H∞ filtering[J]. J. Math. Anal. Appl.,2002. Vol.269:369-381.
[47]Huaizhong Li Minyue Fu, A Linear Matrix Inequality Approach to Robust H∞ Filtering[J]. IEEE Transactions on Signal Processing,1997. Vol.45 (9):2333-2350.
[48]S.H.Jin J.B. Park, Robust H∞ filtering for polytopic uncertain systems via convex optimisation[J]. Control Theory Appl,2001. Vol.148(1):55-59.
[49]高会军,王常虹,参数摄动系统的鲁棒H∞状态估计[J].控制与决策,2004 Vol.19(2)：147-151.
[50]Lihua Xie Lilei Lu, David Zhang, Huanshui Zhang. Robust Filtering for Uncertain Discrete-time Systems:an Improved LMI Approach[C]. in Proceedings of the 42nd IEEE Conference on Decision and Control. Hawaii USA.2003:906-911.
[51]Fu M De Souza C E, Xie L., H∞ estimation for uncertain systems[J]. Int J of Robust and Nonlinear Control,1992. Vol.2(1):87-105.
[52]Carlos E. de Souza Uri Shaked, Minyue Fu, Robust H∞ Filtering for Continuous Time Varying Uncertain Systems with Deterministic Input Signals[J]. IEEE Transactions on Signal Processing,1995. Vol.43(3): 709-719.
[53]K.M.Nagpal P.P.Khargonekar, Filtering and smoothing in a H∞ setting[J]. IEEE Transactions on Automatic Control,1991. Vol.36:152-166.
[54]U.Shaked Y.theodor. H∞ optimal estimation:A tutorial[C]. in Proceeding 31st IEEE conference Decision and control. Tucson, AZ.1992:2278-2286.
[55]Shaked U., H∞ minimum error state estimation of linear stationary processes[J]. IEEE Transactions on Automatic Control,1990. Vol.35: 554-558.
[56]Carlos E. de Souza Minyue Fu, L. Xie, H∞ estimation for discrete-time linear uncertain systems[J]. int. J. of Robust Nonlinear Conrol,1991. Vol.1(1):11-23.
[57]Lihua Xie C.E.de Souza. On robust filtering for linear systems with parameter uncertainty[C]. in Proceedings of the 34th Conference on Decision and control. NEW Orleans, LA.1995:2087-2092.
[58]林岳松,薛安克,钱积新,基于LMI方法的鲁棒H∞滤波器设计[J].电路与系统学报,2004.Vol.9(5)：81-85.
[59]Palhares RM Peres P L D., Robust H∞ filtering design with pole placement constraint via linear matrix inequalities[J]. J of Optimization Theory and Applications,1999. Vol.102(2):239-261.
[60]De Oliveira M C Bernussou J, Geromel J C., A new discrete-time robust stability condition[J]. Systems and Control Letters,1999. Vol.37(2): 261-265.
[61]Shaked U., Improved LMI Representations for the Analysis and the Design of Continuous-Time Systems with Polytopic Type Uncertainty[J]. IEEE Transactions on Automatic Control,2001. Vol.46(4):652-656.
[62]Wang Z Huang B., Robust H2/H∞ filtering for linear systems with error variance constraints[J]. IEEE Transactions on Signal Processing,2000. Vol.48 (8):2463-2467.
[63]Wang Z Unbehauen H., Robust H2/H∞ state estimation for systems with error variance constraints:the continuous-time case[J]. IEEE Trantions on Automatic Control,1999. Vol.44(5):1061-1065.
[64]Palhares R M Peres P L D., LMI Approach to the Mixed H2/H∞ Filtering Design for Discrete-Time Uncertain Systems[J]. IEEE Transactions on Aerospcace and Electronic Systems,2001. Vol.37(1):292-296.
[65]Gao H Lam J, Xie L, New approach to mixed H2/H∞ filtering for polytopic discrete-time systems[J]. IEEE Transactions on Signal Processing,2005. Vol.53(8):3183-3192.
[66]马清亮,胡昌华,不确定连续系统的鲁棒H2/H∞滤波[J].控制与决策,2007.Vol.22(3)：318-321.
[67]Wilson D A., Convolution and Hankel operator norms for linear system[J]. IEEE Transactions on Automatic Control,1989. Vol.34(1):94-97.
[68]刘诗娜,费树岷,冯纯伯,线性不确定系统鲁棒滤波器设计[J].自动化学报,2002.Vol.28(1)：50-55.
[69]金学波,孙优贤,参数不确定系统鲁棒H∞保代价滤波器设计新方法[J].电路与系统学报,2005.Vol.10(4)：116-120.
[70]M.C. de Oliveiraa J. Bernussoub, J.C. Geromela, A new discrete-time robust stability condition[J]. Systems & Control Letters,1999. Vol.37: 261-265.
[71]M. C. de Oliveira R. E. Skelton Stability Tests for Constrained Linear Systems. [J]. Robust Control,2001:241-257.
[72]O. Bachelier J. Bernussou, M. C. de Oliveira. Parameter Dependant Lyapunov Control Design:Numerical Evaluation[C]. in Proceedings of the 38thConference on Decision and Control.1999:293-297.
[73]P. Apkarian H. D. Tuan, J. Bernussou., Continuous-Time Analysis, Eigenstructure Assignment and H2 Synthesis with Enhanced Linear Matrix enqualities(LMI) Characterizations [J]. IEEE Transaction on Automatic Control Theory Appl.,2001. Vol.46(12):1941-1946.
[74]Y. He M. Wu, J. H. She., Improved Bounded-Real-Lemma Representation and H∞ Control of Systems with Polytopic Uncertainties [J]. IEEE Transactions on Circuits and Systems,2005.Vol.52(7):380-383.
[75]Tong Li, Yingmin Jia. Improved LMI Representations for Bounded Real Criterion of Systems with Polytopic Type Uncertainty'[C]. in Proceedings of the American Control Conference. Denver, Colorado.2003:851-856.
[76]Y. Cao Z. Lin., A Descriptor Systems Approach to Robust Stability Analysis and Controller Synthesis[J]. IEEE Transactions on Automatic Control,2004. Vol.49(11):2081-2084.
[77]Fridman E. A Lyapunov-Based Approach to Stability of Descriptor Systems with Delay[C]. in the 40th IEEE Conference on Decision and Control. Oriando, Florida USA.2001 Vol.THA11-2:2850-2855.
[78]Shengyuan Xu Chengwu Yang, Yugang Niu, James Lam, Robust stabilization for uncertain discrete singular system[J]. Automatica,2001. Vol.37:769-774.
[79]Shengyuan Xu James Lam, Chengwu Yang, Robust H∞ control for uncertain discrete singular systems with pole placement in a disk[J]. Systems & Control Letters,2001. Vol.43:85-93.
[80]徐胜元,牛玉刚,杨成梧,参数不确定性奇异系统的鲁棒H∞控制[J].自动化学报,2001.Vol.27(3)：397-400.
[81]Shengyuan Xu Paul Van Dooren, Radu Stefan, and James Lam, Robust Stability and Stabilization for Singular Systems With State Delay and Parameter Uncertainty[J]. IEEE Transactions on Automatic Control,2002. Vol.47 (7):1122-1128.
[82]Terra Joao Yoshiyuki Ishihara and Marco Henrique, On the Lyapunov Theorem for Singular Systems[J]. IEEE Transactions on Automatic Control, 2002. Vol.47(11):1926-1930.
[83]Shengyuan Xu James Lam, and Yun Zou, H∞ Filtering for Singular Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(12):2217-2222.
[84]DONG YUE JAMES LAM, Suboptimal Robust Mixed H2/H∞ Controller Design for Uncertain Descriptor Systems with Distributed Delays[J]. Computers and biathematics with Applications,2004. Vol.47:1041-1055.
[85]鲁仁全,黄文君,苏宏业,褚健,一类不确定Lur'e时滞奇异系统的鲁棒H∞控制[J].自动化学报,2004.Vol.30(6)：920-927.
[86]鲁仁全,苏宏业,褚健,一类Lur'e系统新的绝对稳定性与绝对二次镇定条件[J].浙江大学学报(工学版),2004 Vol.38(2)：129-134.
[87]蔡晨晓,邹云,徐胜元,奇异摄动系统的二次稳定性和二次可镇定性[J].信息与控制,2005.Vol.34(3)：344-349.
[88]Anke Xue Ming Ge, Jingzhong Wang, and Renquan Lu. Robust H-Infinity Filtering for A Class of Uncertain Nonlinear Singular Delay Systems[C].in the 2006 American Control Conference. Minneapolis, Minnesota, USA. 2006 Vol.ThA03.6:2221-2226.
[89]Fong C.-M. Lee and I.K., H∞ optimal singular and normal filter design for uncertain singular systems[J]. IET Control Theory Appl.,2007. Vol.1(1):119-126.
[90]LU Ren-Quan WANG Jun-Hong, XUE An-Ke,SU Hong-Ye,CHU Jian, Robust H∞ Filtering for a Class of Uncertain Lur'e Time-delay Singular Systems[J]. Acta Autoumatica Sinica,2007. Vol.33(3):292-296.
[91]Shengyuan Xu James Lamb, Reduced-order H∞ filtering for singular systems[J]. Systems & Control Letters 2007. Vol.56:48-57.
[92]张光磊,周彤,线性分式扰动下奇异系统鲁棒滤波递推算法[J].自动化学报,2007.Vol.33(11)：1150-1155.
[93]王惠姣,潘海鹏,鲁仁全,一类不确定奇异系统的鲁棒H∞控制[J].浙江大学学报(工学版),2007.Vol.41(10)：1688-1691.
[94]Aline F. Bianco Joao Y. Ishihara, Marco H. Terra. Optimal Robust Prediction for General Discrete Time Singular Systems[C]. in 10th Intl. Conf. on Control, Automation, Robotics and Vision. Hanoi, Vietnam. 2008:1793-1798.
[95]Carlos E. de Souza Karina A. Barbosa, Minyue Fu, Robust filtering for uncertain linear discrete-time descriptor systems[J]. Automatica 2008. Vol.44:792-798.
[96]Joao Y Ishiharaa Marco H. Terrab, Robust state prediction for descriptor systems[J]. Automatica,2008. Vol.44:2185-2190.
[97]WANG Hui-Jiao LIN Yue Song, XUE An-Ke,PAN Hai-Peng,LU Ren-Quan, Reliable Robust H∞ Tracking Control for a Class of Uncertain Lur'e Singular Sysrems[J]. Acta Autoumatica Sinica,2008. Vol.34(8):893-898.
[98]陈凌,曾建平,奇异系统的降阶H∞滤波器的设计[J].厦门大学学报(自然科学版),2008.Vol.47(4)：489-494.
[99]Xu Tianqun Chen Yuepeng, Zhang Jingxin, Liu Huanbin, Xu Tianhe. All H∞ Singular and Normal Filter Design for Uncertain Singular Systems[C]. in Chinese Control and Decision Conference.2009 3134-2139.
[100]Dai L, ed. Singular Control.1989, Berlin:Springer-Verlag.
[101]Masubuchi I Suda N, Ohara A. LIMI-based controller synthesis:a unfied formulation and solution[C]. in Proc. American Control Conf. 1995:3467-3477.
[102]Masubuchi I Kamitane Y, Control for Descriptor Systems:A Matrix Inequalities Approach[J]. Automatica,1997. Vol.33:669-673.
[103]Lam J Xu s, Zhang L, Robust D-stability analysis for uncertain discrete singular systems with state delay[J]. IEEE Trans. Circuits syst. I.,2002. Vol.49(551-555).
[104]Hassibi B., Sayed, A. H., & Kailath, T., Indefinite quadratic estimation and control:A unified approach to H2 and H∞ theories[J]. SIAM studies in applied mathematics series,1998.
[105]张焕水,邓自立,广义离散随机线性系统自校正最优预报器[J].自动化学报,1996.Vol.22(1)：49-57.
[106]张焕水,柴天佑,广义离散随机线性系统最有滤波、预报和平滑估计的统一格式[J].控制理论与应用,1997.Vol.14(5)：723-726.
[107]Huanshui Zhang David Zhang, Lihua Xie. H∞ Fixed-Lag Smoothing and Prediction for Linear Continous-Time Systems[C]. in the American Control Conference. Denver, Colorado.2003:4201-4206.
[108]Huanshui Zhang Lihua Xieb, Yeng Chai Soh, Risk-sensitive filtering, prediction and smoothing for discrete-time singular systems[J]. Automatica, 2003. Vol.39:57-66.
[109]Huanshui Zhang DavidZhang, Lihua Xie, An innovation approach to H∞ prediction for continuous-time systems with application to systems with delayed measurements[J]. Automatica,2004. Vol.40:1253-1261.
[110]王好谦,张焕水,段广仁,王高才,广义系统H∞多步预报器设计[J].控制理论与应用,2007.Vol.24(5)：693-700.
[111]Emilia Fridman and Uri Shaked, An Improved Delay-Dependent H∞ Filtering of Linear Neutral Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(3):668-673.
[112]H. J. Gao C. H. Wang, Delay-Dependent Robust H∞ and L2-L∞ Filtering for a Class of Uncertain Nonlinear Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(9):1661-1666.
[113]H. J. Gao C. H. Wang, A Delay-Dependent Approach to Robust H∞ Filtering for Uncertain Discrete-Time State-Delayed Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(6):1631-1640.
[114]E. Fridman and Uri Shaked, A New H∞ Filter Design for Linear Time Delay Systems[J]. IEEE Transactions on Signal Processing,2001. Vol.49(11):2839-2843.
[115]E. Fridman and U. Shaked, New Bounded Real Lemma Representations for Time-Delay Systems and Their Applications[J]. IEEE Transactions on Automatic Control,2001. Vol.46(12):1973-1979.
[116]Emilia Fridman, Uri Shaked, An Improved Stabilization Method for Linear Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2002. Vol.47(11):1931-1937.
[117]E. Fridman U. Shaked, and L. Xie, Robust H∞ Filtering of Linear Systems With Time-Varying Delay[J]. IEEE Transactions on Automatic Control, 2003.Vol.48(1):159-165.
[118]E. Fridman and U. Shaked, Parameter Dependent Stability and Stabilization of Uncertain Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(5):861-866.
[119]Yong He Guo-Ping Liu, D. Rees, Min Wu,H∞ filtering for discrete-time systems with time-varying delay[J]. Signal Processing,2008:1-21.
[120]王俊玲,王常虹,高会军,一类时滞LPV系统的鲁棒H∞滤波[J].哈尔滨工程大学学报,2004.Vol.25(1)：62-68.
[121]何勇,吴敏,多时变时滞系统的鲁棒稳定及有界实引理的时滞相关条件[J].控制理论与应用,2004.Vol.21(5)：735-741.
[122]Carlos E. DE Souzab Reinaldo M. Palharess, Pedro L. D. Pereso. Robust H∞ Filtering for Uncertain Linear Systems with Multiple Time-Varying State Delays:An LMI Approach[C]. in the 38th Conference on Decision & Control. Phoenix, Arizona USA.1999 Vol.WeM08:2023-2028.
[123]R. Palhares P.Peres, C.de Souza. Robust H∞ filtering for linear continuous-time uncertain systems with multiple delays:An LMI approach[C]. in the 3rd IFAC Conf. Robust Control Design. Prague, Czech Republic.2000.
[124]P.PARK, A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Transactions on Automatic Control,1999. Vol.44 (4):876-877.
[125]Emilia Fridman and Uri Shaked, An Improved Delay-Dependent H∞ Filtering of Linear Neutral Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(3):668-673.
[126]International Towing Tank Conference—ITTC Symbols and Terminology List Final Version 1996 May 13 1997.
[127]陶尧森编著,船舶耐波性.1996,上海：上海交通大学出版社.
[128]赵希人,陈虹丽,叶葵,魏东,基于扩展卡尔曼滤波的船舶纵向运动受扰力与力矩的估计[J].中国造船,2004.Vol.45(3)：24-30.
[129]赵希人,唐慧妍,王宪荣,彭秀艳,船舶横向运动受扰力与受扰力矩估计[J].船舶力学,2004.Vol.8(4)：35-41.
[130]周正全,缪国平.船舶运动的理论预报[C].in《中国造船》增刊,船舶耐波性专集.中国造船工程学会.1991.
[131]金鸿章,姚绪梁,船舶控制原理.2001,哈尔滨：哈尔滨工程大学出版社.
[132]陈虹丽,基于π型舵船舶纵向多变量随机控制方法研究[D].博士学位论文.2004,哈尔滨：哈尔滨工程大学.
[133]Xianfeng Wang Xiren Zhao, Xiuyan Peng, Hongfang Sun. Statistic Model for LQG Control of Ship Longitudinal Mition[C]. in 1st International Symposium on Systems and Control in Aerospace and Astronautics. Harbin, China.2006 Vol.2:1171-1174.
[134]赵希人,孙宏放,屈阳,船舶运动与受扰Kalman估计精度的统计分析[J].系统仿真学报,2008.Vol.20(18)：4795-4797.
[135]赵希人,彭秀艳,尹中凤,基于水动力系数摄动的船舶横向运动姿态与受扰Kalman滤波的统计建模[J].船舶力学,2007.Vol.11(5)：702-707.
[136]赵希人,彭秀艳,尹中凤,船舶横向运动姿态及受扰卡尔曼估计的鲁棒性能概率建模[J].仪器仪表学报,2005.Vol.26：885-889.
[137]俞立,鲁棒控制-线性矩阵不等式处理方法.2002,北京：清华大学出版社.
[138]吴敏,桂卫华,何勇,现代鲁棒控制.2006,长沙：中南大学出版社.
[139]黄玉林,张维海,李庆华,一类非线性随机不确定系统的鲁棒滤波[J].山东大学学报(理学版),2006.Vol.41(2)：78-84.
[140]何朕,王广雄,王西田,于达仁,参数不确定系统的鲁棒H∞估计[J].控制理论与应用,2001.Vol.18：115-117.
[141]王广雄,李连锋,王新生,鲁棒设计中参数不确定性的描述[J].电机与控制学报,2001.Vol.5(1)：5-7.
[142]PETERSEN I.R., ANDERSON, B.D.O., and JONCKHEERE, E.A., A first principlies solution to the nonsingular H∞ control problem[J]. Int. J. Robust Nonlinear Control,1991. Vol.1:171-185.
[143]Xie L., Output feedback H∞ control of systems with parameter uncertainty[J].Int. J. of Control,1996. Vol.63(4):741-750.
[144]赵希人,陈虹丽,艾晓庸,沈艳,于秀萍,船舶运动纵向受扰力和受扰力矩估计方法研究[J].哈尔滨工程大学学报,2004.Vol.25(2)：167-170.
[145]IZUMI MASUBUCHI YOSHIYUKI KAMITANE, ATSUMI OHARA and NQBUHIDE SUDA, H∞ Control for Descriptor Systems:A Matrix Inequalities Approach[J]. Automatica,1997.Vol.33(4):669-673.
[146]鲁仁全,不确定Lur'e时滞系统的鲁棒控制研究[D].浙江大学博士论文.2004.
[2]Fleek, J.T. Short Time Prediction of the Motion of a Ship in Waves[C]. in Proc.Ist Conf. On Ships and Waves. Couneil on Wave Research and SNAME.1954.
[3]Bates M.R., Book, D. H. and Powell, F.D., Analog Computer Applications in Predictor Design[J]. IRE Trans. On Elec. Com.,1957. Vol.6(3).
[4]Kaplan P., Sargent, T. P., Theoretical Study of the Motions of the an Aircraft Carrier at Sea[R]. Oceanics,Inc.1965. January, No.65-22.
[5]Kaplan P., Sargent, T. P., A Preliminary Study of Prediction Techniques for Aircraft Carrier Motions SRpt[R].ea,Oceanics,Inc.1965.6:5-23.
[6]Kaplan P. A Study of Prediction Techniques for Aircraft Carrier Motions at Sea[C]. in AIAA 6th ASM.1968 Vol.No.68-123.
[7]Kaplan P., Ross, D. Comparative Performance of wave Measuring systems Mounted on ships in Motion at sea[C]. in 4th National Symp. of Marine Science Inst. ISA,Coco Beach,Florida.1968.
[8]Kalman R.E and Bucy, R.S., New Results in Linear Filtering and Prediction Theory[J]. Transactions of ASME, Journal of Basic Engineering Series, 1961.Vol.83D:95-108.
[9]MENAHEM M.SIDAR BRIAN F.DOOLIN, On the Feasibility of Real-Time Prediction of Aircraft Carrier Motiona at Sea[J]. IEEE Transactions on Automatic Control,1983. Vol.AC-28(3):350-356.
[10]Triantafyllou M., Bodson,M. Real Time Predilection of Marine Vessel Motion Using Kalman Filtering Techniques[C]. in Proc. OTC. Houston,Texas.1982 Vol.
[11]Triantafyllou M. Athans M. Real Time Estimation of the Heaving and Pitching Motions of a Ship Using a Kalman Filter[C]. in Proc. Oeeanics 81. Boston MA. Sep.1981.
[12]M. Triantafyllou, Real Time Prediction and Estimation of Ship Motion Using Kalman Filtering Techniques[R]. NASA-CT-169284 1982. No.82-31637.
[13]Triantaryllou M. Athans M., Real Time Estimation of Motions of a Destroyer Using Kalman Filtering Techniques[R]. Laboratory for information and Decision Systems MIT Cambridge. MAY,1983.
[14]Enochson. The Predietion of ShiP Motion at Sea[C]. in CTC.1963.
[15]Dazell J. F., A Nile on short-time Prediction of ship Motions,[J]. Journal of ship Research,1965. Vol.9(2):48-52.
[16]戴仰山,宋竞正,李维扬,快艇在海浪中的运动[J].哈尔滨工程大学学报1981(02).
[17]Yumon I., Real Time Prediction of Ship Response to Ocean Waves Using Time Series Analysis[J]. OCEANS,1981. Vol.13:1082-1089.
[18]Khan A., Bil, C., Marion,K.E., Ship motion prediction for launch and recovery of air vehicles[J]. OCEANS,2005. Vol.32795-2801.
[19]SUN Li-hong SHEN Ji-hong. Prediction of Ship Pitching Based on Support Vector Machines[C]. in International Conference on Computer Engineering and Technology.2009 Vol.1:380-382.
[20]Nicolau V., Aiordachioaie, D., Popa, R. Neural network prediction of the wave influence on the yaw motion of a ship[C]. in IEEE International Joint Conference on Neural Networks.2004 Vol.4:2801-2806.
[21]虞兰生,戴遗山,船舶运动的自适应预报[J].中国造船,1988.Vol.10(2)：83-86.
[22]郜焕秋,谢楠,盛万安,应用人工神经网络理论的船舶运动包络预报方法[J].中国造船,1994(3)：11-20.
[23]郜焕秋,刘楚学.海上实船运动的极短期预报可行性研究[C].in第四届船舶耐波性学术讨论会论文集.中国造船工程学会.1986.
[24]周淑秋,赵希人,舰船航态极短期预报的非线性方法[J].哈尔滨工程大学学报,1996.Vol.17(4)：1-7.
[25]冯铁城,吴善勤,雷振华,浮式海洋平台运动实时预报[J].海洋工程,1991.Vol.9(3)：23-28.
[26]彭秀艳,船舶在线姿态预报及仿真技术研究[D].自动化学院.博士学位论文.2006,哈尔滨：哈尔滨工程大学.
[27]彭秀艳,赵希人,吕淑萍,魏纳新,具有艏前波观测量的大型舰船姿态 运动预报[J].系统仿真学报,2002.Vol.14(6)：809-814.
[28]谢美萍,沈艳,彭秀艳,赵希人,舰船运动的一种改进经典谱估计方法[J].船舶工程,2000(4)：6-8.
[29]谢美萍,赵希人,基于投影寻踪学习的大型船舶运动极短期预报[J].船舶力学,2000.Vol.4(4)：28-32.
[30]沈继红,尚寿亭,赵希人,舰船纵摇运动函数变换型GM(1,1)模型研究[J].哈尔滨工业大学学报,2001(3).
[31]沈继红,赵希人,利用最小二乘法改进GM(2,1)模型[J].哈尔滨工程大学学报,2001(4)：64-66.
[32]谢美萍,赵希人,基于小波网的船舶运动极短期建模预报[J].船舶力学,2002.Vol.6(2)：15-21.
[33]马洁,刘小河,李国斌,韩志刚,大型舰船纵摇运动的多层递阶预报[J].船舶工程,2006.Vol.28(1)：5-8.
[34]李晖,郭晨,金鸿章,基于WT和MGFPE混合模式的船舶横摇运动长期预测[J].哈尔滨工程大学学报2007.Vol.28(6)：611-615.
[35]孙李红,沈继红,基于改进GM(1,1)模型的舰船纵摇运动预报[J].哈尔滨工程大学学报,2009.Vol.30(3)：287-291.
[36]Friedman J.H., Tukey,J. W., A projection pursuit algorithm for exploratory data analysis[J]. IEEE Trans. Computers,1974. Vol.C-23:881-889.
[37]沈继红,灰色系统理论预测方法研究及其在舰船运动预报中的应用[D].自动化学院.博士学位论文.2001,哈尔滨：哈尔滨工程大学.
[38]张汉国,张洪钺,有关鲁棒状态估计的研究评述[J].北京航天航空大学学报,1992(4)：91-97.
[39]邓自立,王建国,非线性系统的自适应推广KALMAN滤波[J].自动化学报,1987.Vol.13(5)：375-379.
[40]张洪才,张友民,贺志斌,一种鲁棒自适应推广Kalman滤波及其在飞行状态估计中的应用[J].信息与控制,1992.Vol.21(6)：343-347.
[41]王司,邓正隆,基于Krein空间的鲁棒Kalman滤波在传递对准中的应用研究[J].中国惯性技术学报,2006.Vol.14(4)：7-11.
[42]Zames G., Feedback and Optimal Sensitivity:Model Reference Transformations Multiplicative Seminorms and Approximant Inverses[J]. IEEE Trans. On Automatic Control,1981. Vol.26:301-320.
[43]Elsayed A, Grimble, M.J., Ho, D. On H∞ filtering in multivariable discrete-time systems[C]. in IEEE International Symposium on Circuits and Systems.1988 Vol.2:1573-1576.
[44]Soura Dasgupta Minyue Fu, Chris Schwarz, Robust Relative Stability of Time-Invariant and Time-Varying Lattice Filters[J]. IEEE Transactions on Signal Processing,1998. Vol.46(8):2088-2100.
[45]U. Shaked N. Berman,H∞ Nonlinear Filtering of Discrete-Time Processes[J]. IEEE Transactions on Signal Processing,1995. Vol.43(9): 2205-2209.
[46]MagdiS.Mahmoud, Discrete-time systems with linear parameter-varying: stability and H∞ filtering[J]. J. Math. Anal. Appl.,2002. Vol.269:369-381.
[47]Huaizhong Li Minyue Fu, A Linear Matrix Inequality Approach to Robust H∞ Filtering[J]. IEEE Transactions on Signal Processing,1997. Vol.45 (9):2333-2350.
[48]S.H.Jin J.B. Park, Robust H∞ filtering for polytopic uncertain systems via convex optimisation[J]. Control Theory Appl,2001. Vol.148(1):55-59.
[49]高会军,王常虹,参数摄动系统的鲁棒H∞状态估计[J].控制与决策,2004 Vol.19(2)：147-151.
[50]Lihua Xie Lilei Lu, David Zhang, Huanshui Zhang. Robust Filtering for Uncertain Discrete-time Systems:an Improved LMI Approach[C]. in Proceedings of the 42nd IEEE Conference on Decision and Control. Hawaii USA.2003:906-911.
[51]Fu M De Souza C E, Xie L., H∞ estimation for uncertain systems[J]. Int J of Robust and Nonlinear Control,1992. Vol.2(1):87-105.
[52]Carlos E. de Souza Uri Shaked, Minyue Fu, Robust H∞ Filtering for Continuous Time Varying Uncertain Systems with Deterministic Input Signals[J]. IEEE Transactions on Signal Processing,1995. Vol.43(3): 709-719.
[53]K.M.Nagpal P.P.Khargonekar, Filtering and smoothing in a H∞ setting[J]. IEEE Transactions on Automatic Control,1991. Vol.36:152-166.
[54]U.Shaked Y.theodor. H∞ optimal estimation:A tutorial[C]. in Proceeding 31st IEEE conference Decision and control. Tucson, AZ.1992:2278-2286.
[55]Shaked U., H∞ minimum error state estimation of linear stationary processes[J]. IEEE Transactions on Automatic Control,1990. Vol.35: 554-558.
[56]Carlos E. de Souza Minyue Fu, L. Xie, H∞ estimation for discrete-time linear uncertain systems[J]. int. J. of Robust Nonlinear Conrol,1991. Vol.1(1):11-23.
[57]Lihua Xie C.E.de Souza. On robust filtering for linear systems with parameter uncertainty[C]. in Proceedings of the 34th Conference on Decision and control. NEW Orleans, LA.1995:2087-2092.
[58]林岳松,薛安克,钱积新,基于LMI方法的鲁棒H∞滤波器设计[J].电路与系统学报,2004.Vol.9(5)：81-85.
[59]Palhares RM Peres P L D., Robust H∞ filtering design with pole placement constraint via linear matrix inequalities[J]. J of Optimization Theory and Applications,1999. Vol.102(2):239-261.
[60]De Oliveira M C Bernussou J, Geromel J C., A new discrete-time robust stability condition[J]. Systems and Control Letters,1999. Vol.37(2): 261-265.
[61]Shaked U., Improved LMI Representations for the Analysis and the Design of Continuous-Time Systems with Polytopic Type Uncertainty[J]. IEEE Transactions on Automatic Control,2001. Vol.46(4):652-656.
[62]Wang Z Huang B., Robust H2/H∞ filtering for linear systems with error variance constraints[J]. IEEE Transactions on Signal Processing,2000. Vol.48 (8):2463-2467.
[63]Wang Z Unbehauen H., Robust H2/H∞ state estimation for systems with error variance constraints:the continuous-time case[J]. IEEE Trantions on Automatic Control,1999. Vol.44(5):1061-1065.
[64]Palhares R M Peres P L D., LMI Approach to the Mixed H2/H∞ Filtering Design for Discrete-Time Uncertain Systems[J]. IEEE Transactions on Aerospcace and Electronic Systems,2001. Vol.37(1):292-296.
[65]Gao H Lam J, Xie L, New approach to mixed H2/H∞ filtering for polytopic discrete-time systems[J]. IEEE Transactions on Signal Processing,2005. Vol.53(8):3183-3192.
[66]马清亮,胡昌华,不确定连续系统的鲁棒H2/H∞滤波[J].控制与决策,2007.Vol.22(3)：318-321.
[67]Wilson D A., Convolution and Hankel operator norms for linear system[J]. IEEE Transactions on Automatic Control,1989. Vol.34(1):94-97.
[68]刘诗娜,费树岷,冯纯伯,线性不确定系统鲁棒滤波器设计[J].自动化学报,2002.Vol.28(1)：50-55.
[69]金学波,孙优贤,参数不确定系统鲁棒H∞保代价滤波器设计新方法[J].电路与系统学报,2005.Vol.10(4)：116-120.
[70]M.C. de Oliveiraa J. Bernussoub, J.C. Geromela, A new discrete-time robust stability condition[J]. Systems & Control Letters,1999. Vol.37: 261-265.
[71]M. C. de Oliveira R. E. Skelton Stability Tests for Constrained Linear Systems. [J]. Robust Control,2001:241-257.
[72]O. Bachelier J. Bernussou, M. C. de Oliveira. Parameter Dependant Lyapunov Control Design:Numerical Evaluation[C]. in Proceedings of the 38thConference on Decision and Control.1999:293-297.
[73]P. Apkarian H. D. Tuan, J. Bernussou., Continuous-Time Analysis, Eigenstructure Assignment and H2 Synthesis with Enhanced Linear Matrix enqualities(LMI) Characterizations [J]. IEEE Transaction on Automatic Control Theory Appl.,2001. Vol.46(12):1941-1946.
[74]Y. He M. Wu, J. H. She., Improved Bounded-Real-Lemma Representation and H∞ Control of Systems with Polytopic Uncertainties [J]. IEEE Transactions on Circuits and Systems,2005.Vol.52(7):380-383.
[75]Tong Li, Yingmin Jia. Improved LMI Representations for Bounded Real Criterion of Systems with Polytopic Type Uncertainty'[C]. in Proceedings of the American Control Conference. Denver, Colorado.2003:851-856.
[76]Y. Cao Z. Lin., A Descriptor Systems Approach to Robust Stability Analysis and Controller Synthesis[J]. IEEE Transactions on Automatic Control,2004. Vol.49(11):2081-2084.
[77]Fridman E. A Lyapunov-Based Approach to Stability of Descriptor Systems with Delay[C]. in the 40th IEEE Conference on Decision and Control. Oriando, Florida USA.2001 Vol.THA11-2:2850-2855.
[78]Shengyuan Xu Chengwu Yang, Yugang Niu, James Lam, Robust stabilization for uncertain discrete singular system[J]. Automatica,2001. Vol.37:769-774.
[79]Shengyuan Xu James Lam, Chengwu Yang, Robust H∞ control for uncertain discrete singular systems with pole placement in a disk[J]. Systems & Control Letters,2001. Vol.43:85-93.
[80]徐胜元,牛玉刚,杨成梧,参数不确定性奇异系统的鲁棒H∞控制[J].自动化学报,2001.Vol.27(3)：397-400.
[81]Shengyuan Xu Paul Van Dooren, Radu Stefan, and James Lam, Robust Stability and Stabilization for Singular Systems With State Delay and Parameter Uncertainty[J]. IEEE Transactions on Automatic Control,2002. Vol.47 (7):1122-1128.
[82]Terra Joao Yoshiyuki Ishihara and Marco Henrique, On the Lyapunov Theorem for Singular Systems[J]. IEEE Transactions on Automatic Control, 2002. Vol.47(11):1926-1930.
[83]Shengyuan Xu James Lam, and Yun Zou, H∞ Filtering for Singular Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(12):2217-2222.
[84]DONG YUE JAMES LAM, Suboptimal Robust Mixed H2/H∞ Controller Design for Uncertain Descriptor Systems with Distributed Delays[J]. Computers and biathematics with Applications,2004. Vol.47:1041-1055.
[85]鲁仁全,黄文君,苏宏业,褚健,一类不确定Lur'e时滞奇异系统的鲁棒H∞控制[J].自动化学报,2004.Vol.30(6)：920-927.
[86]鲁仁全,苏宏业,褚健,一类Lur'e系统新的绝对稳定性与绝对二次镇定条件[J].浙江大学学报(工学版),2004 Vol.38(2)：129-134.
[87]蔡晨晓,邹云,徐胜元,奇异摄动系统的二次稳定性和二次可镇定性[J].信息与控制,2005.Vol.34(3)：344-349.
[88]Anke Xue Ming Ge, Jingzhong Wang, and Renquan Lu. Robust H-Infinity Filtering for A Class of Uncertain Nonlinear Singular Delay Systems[C].in the 2006 American Control Conference. Minneapolis, Minnesota, USA. 2006 Vol.ThA03.6:2221-2226.
[89]Fong C.-M. Lee and I.K., H∞ optimal singular and normal filter design for uncertain singular systems[J]. IET Control Theory Appl.,2007. Vol.1(1):119-126.
[90]LU Ren-Quan WANG Jun-Hong, XUE An-Ke,SU Hong-Ye,CHU Jian, Robust H∞ Filtering for a Class of Uncertain Lur'e Time-delay Singular Systems[J]. Acta Autoumatica Sinica,2007. Vol.33(3):292-296.
[91]Shengyuan Xu James Lamb, Reduced-order H∞ filtering for singular systems[J]. Systems & Control Letters 2007. Vol.56:48-57.
[92]张光磊,周彤,线性分式扰动下奇异系统鲁棒滤波递推算法[J].自动化学报,2007.Vol.33(11)：1150-1155.
[93]王惠姣,潘海鹏,鲁仁全,一类不确定奇异系统的鲁棒H∞控制[J].浙江大学学报(工学版),2007.Vol.41(10)：1688-1691.
[94]Aline F. Bianco Joao Y. Ishihara, Marco H. Terra. Optimal Robust Prediction for General Discrete Time Singular Systems[C]. in 10th Intl. Conf. on Control, Automation, Robotics and Vision. Hanoi, Vietnam. 2008:1793-1798.
[95]Carlos E. de Souza Karina A. Barbosa, Minyue Fu, Robust filtering for uncertain linear discrete-time descriptor systems[J]. Automatica 2008. Vol.44:792-798.
[96]Joao Y Ishiharaa Marco H. Terrab, Robust state prediction for descriptor systems[J]. Automatica,2008. Vol.44:2185-2190.
[97]WANG Hui-Jiao LIN Yue Song, XUE An-Ke,PAN Hai-Peng,LU Ren-Quan, Reliable Robust H∞ Tracking Control for a Class of Uncertain Lur'e Singular Sysrems[J]. Acta Autoumatica Sinica,2008. Vol.34(8):893-898.
[98]陈凌,曾建平,奇异系统的降阶H∞滤波器的设计[J].厦门大学学报(自然科学版),2008.Vol.47(4)：489-494.
[99]Xu Tianqun Chen Yuepeng, Zhang Jingxin, Liu Huanbin, Xu Tianhe. All H∞ Singular and Normal Filter Design for Uncertain Singular Systems[C]. in Chinese Control and Decision Conference.2009 3134-2139.
[100]Dai L, ed. Singular Control.1989, Berlin:Springer-Verlag.
[101]Masubuchi I Suda N, Ohara A. LIMI-based controller synthesis:a unfied formulation and solution[C]. in Proc. American Control Conf. 1995:3467-3477.
[102]Masubuchi I Kamitane Y, Control for Descriptor Systems:A Matrix Inequalities Approach[J]. Automatica,1997. Vol.33:669-673.
[103]Lam J Xu s, Zhang L, Robust D-stability analysis for uncertain discrete singular systems with state delay[J]. IEEE Trans. Circuits syst. I.,2002. Vol.49(551-555).
[104]Hassibi B., Sayed, A. H., & Kailath, T., Indefinite quadratic estimation and control:A unified approach to H2 and H∞ theories[J]. SIAM studies in applied mathematics series,1998.
[105]张焕水,邓自立,广义离散随机线性系统自校正最优预报器[J].自动化学报,1996.Vol.22(1)：49-57.
[106]张焕水,柴天佑,广义离散随机线性系统最有滤波、预报和平滑估计的统一格式[J].控制理论与应用,1997.Vol.14(5)：723-726.
[107]Huanshui Zhang David Zhang, Lihua Xie. H∞ Fixed-Lag Smoothing and Prediction for Linear Continous-Time Systems[C]. in the American Control Conference. Denver, Colorado.2003:4201-4206.
[108]Huanshui Zhang Lihua Xieb, Yeng Chai Soh, Risk-sensitive filtering, prediction and smoothing for discrete-time singular systems[J]. Automatica, 2003. Vol.39:57-66.
[109]Huanshui Zhang DavidZhang, Lihua Xie, An innovation approach to H∞ prediction for continuous-time systems with application to systems with delayed measurements[J]. Automatica,2004. Vol.40:1253-1261.
[110]王好谦,张焕水,段广仁,王高才,广义系统H∞多步预报器设计[J].控制理论与应用,2007.Vol.24(5)：693-700.
[111]Emilia Fridman and Uri Shaked, An Improved Delay-Dependent H∞ Filtering of Linear Neutral Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(3):668-673.
[112]H. J. Gao C. H. Wang, Delay-Dependent Robust H∞ and L2-L∞ Filtering for a Class of Uncertain Nonlinear Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(9):1661-1666.
[113]H. J. Gao C. H. Wang, A Delay-Dependent Approach to Robust H∞ Filtering for Uncertain Discrete-Time State-Delayed Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(6):1631-1640.
[114]E. Fridman and Uri Shaked, A New H∞ Filter Design for Linear Time Delay Systems[J]. IEEE Transactions on Signal Processing,2001. Vol.49(11):2839-2843.
[115]E. Fridman and U. Shaked, New Bounded Real Lemma Representations for Time-Delay Systems and Their Applications[J]. IEEE Transactions on Automatic Control,2001. Vol.46(12):1973-1979.
[116]Emilia Fridman, Uri Shaked, An Improved Stabilization Method for Linear Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2002. Vol.47(11):1931-1937.
[117]E. Fridman U. Shaked, and L. Xie, Robust H∞ Filtering of Linear Systems With Time-Varying Delay[J]. IEEE Transactions on Automatic Control, 2003.Vol.48(1):159-165.
[118]E. Fridman and U. Shaked, Parameter Dependent Stability and Stabilization of Uncertain Time-Delay Systems[J]. IEEE Transactions on Automatic Control,2003. Vol.48(5):861-866.
[119]Yong He Guo-Ping Liu, D. Rees, Min Wu,H∞ filtering for discrete-time systems with time-varying delay[J]. Signal Processing,2008:1-21.
[120]王俊玲,王常虹,高会军,一类时滞LPV系统的鲁棒H∞滤波[J].哈尔滨工程大学学报,2004.Vol.25(1)：62-68.
[121]何勇,吴敏,多时变时滞系统的鲁棒稳定及有界实引理的时滞相关条件[J].控制理论与应用,2004.Vol.21(5)：735-741.
[122]Carlos E. DE Souzab Reinaldo M. Palharess, Pedro L. D. Pereso. Robust H∞ Filtering for Uncertain Linear Systems with Multiple Time-Varying State Delays:An LMI Approach[C]. in the 38th Conference on Decision & Control. Phoenix, Arizona USA.1999 Vol.WeM08:2023-2028.
[123]R. Palhares P.Peres, C.de Souza. Robust H∞ filtering for linear continuous-time uncertain systems with multiple delays:An LMI approach[C]. in the 3rd IFAC Conf. Robust Control Design. Prague, Czech Republic.2000.
[124]P.PARK, A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Transactions on Automatic Control,1999. Vol.44 (4):876-877.
[125]Emilia Fridman and Uri Shaked, An Improved Delay-Dependent H∞ Filtering of Linear Neutral Systems[J]. IEEE Transactions on Signal Processing,2004. Vol.52(3):668-673.
[126]International Towing Tank Conference—ITTC Symbols and Terminology List Final Version 1996 May 13 1997.
[127]陶尧森编著,船舶耐波性.1996,上海：上海交通大学出版社.
[128]赵希人,陈虹丽,叶葵,魏东,基于扩展卡尔曼滤波的船舶纵向运动受扰力与力矩的估计[J].中国造船,2004.Vol.45(3)：24-30.
[129]赵希人,唐慧妍,王宪荣,彭秀艳,船舶横向运动受扰力与受扰力矩估计[J].船舶力学,2004.Vol.8(4)：35-41.
[130]周正全,缪国平.船舶运动的理论预报[C].in《中国造船》增刊,船舶耐波性专集.中国造船工程学会.1991.
[131]金鸿章,姚绪梁,船舶控制原理.2001,哈尔滨：哈尔滨工程大学出版社.
[132]陈虹丽,基于π型舵船舶纵向多变量随机控制方法研究[D].博士学位论文.2004,哈尔滨：哈尔滨工程大学.
[133]Xianfeng Wang Xiren Zhao, Xiuyan Peng, Hongfang Sun. Statistic Model for LQG Control of Ship Longitudinal Mition[C]. in 1st International Symposium on Systems and Control in Aerospace and Astronautics. Harbin, China.2006 Vol.2:1171-1174.
[134]赵希人,孙宏放,屈阳,船舶运动与受扰Kalman估计精度的统计分析[J].系统仿真学报,2008.Vol.20(18)：4795-4797.
[135]赵希人,彭秀艳,尹中凤,基于水动力系数摄动的船舶横向运动姿态与受扰Kalman滤波的统计建模[J].船舶力学,2007.Vol.11(5)：702-707.
[136]赵希人,彭秀艳,尹中凤,船舶横向运动姿态及受扰卡尔曼估计的鲁棒性能概率建模[J].仪器仪表学报,2005.Vol.26：885-889.
[137]俞立,鲁棒控制-线性矩阵不等式处理方法.2002,北京：清华大学出版社.
[138]吴敏,桂卫华,何勇,现代鲁棒控制.2006,长沙：中南大学出版社.
[139]黄玉林,张维海,李庆华,一类非线性随机不确定系统的鲁棒滤波[J].山东大学学报(理学版),2006.Vol.41(2)：78-84.
[140]何朕,王广雄,王西田,于达仁,参数不确定系统的鲁棒H∞估计[J].控制理论与应用,2001.Vol.18：115-117.
[141]王广雄,李连锋,王新生,鲁棒设计中参数不确定性的描述[J].电机与控制学报,2001.Vol.5(1)：5-7.
[142]PETERSEN I.R., ANDERSON, B.D.O., and JONCKHEERE, E.A., A first principlies solution to the nonsingular H∞ control problem[J]. Int. J. Robust Nonlinear Control,1991. Vol.1:171-185.
[143]Xie L., Output feedback H∞ control of systems with parameter uncertainty[J].Int. J. of Control,1996. Vol.63(4):741-750.
[144]赵希人,陈虹丽,艾晓庸,沈艳,于秀萍,船舶运动纵向受扰力和受扰力矩估计方法研究[J].哈尔滨工程大学学报,2004.Vol.25(2)：167-170.
[145]IZUMI MASUBUCHI YOSHIYUKI KAMITANE, ATSUMI OHARA and NQBUHIDE SUDA, H∞ Control for Descriptor Systems:A Matrix Inequalities Approach[J]. Automatica,1997.Vol.33(4):669-673.
[146]鲁仁全,不确定Lur'e时滞系统的鲁棒控制研究[D].浙江大学博士论文.2004.