摘要
在描述交链大系统,机械多体系统,电力系统等时,广义系统模型是一个更方便更自然的方法。作为一种方法,广义系统模型已经在获得一些复杂系统的鲁棒稳定性和鲁棒性能分析中得到广泛应用。因此,广义系统的研究无论从理论还是应用上都是非常重要的。
广义系统与正常系统的一个最大区别就是系统响应可能含有脉冲,这可能给实际系统造成很大的破坏甚至摧毁系统。因此对脉冲消除的研究是非常必要的。另外,对实际系统来说,并不是所有的系统状态都能量测得到,这样就限制了状态反馈控制律的使用。为了克服这个障碍,一个可能的方法就是先通过观测器估计系统的状态然后再根据估计的状态设计控制律。为了保证观测器估计的准确性也要求观测器系统不含脉冲模。由于这些原因,本论文系统深刻地讨论广义线性系统的脉冲消除和观测器设计问题,其主要结果如下:
一、对方广义系统考虑了通过最一般的控制器—动态输出反馈控制器的正则化。根据原始的系统矩阵建立了三类可正则化条件。而且进一步显示,对于可正则系统,所有正则化控制器的集合形成一个Zariski开集。
二、考虑了通过状态反馈和PD状态反馈的脉冲消除问题。基于导数反馈标准型给出了使闭环系统无脉冲的状态反馈的参数化表示。为了考虑PD反馈脉冲消除问题,对方广义系统和非方广义系统分别提出了可I-能控性和可脉冲模能控性的概念。结论显示,可I-能控性和可脉冲模能控性分别是方广义系统和非方广义系统的PD反馈消除脉冲的充要条件。根据原始系统矩阵建立了两类可I-能控性和可脉冲模能控性判据,而且给出了闭环系统可达到的动态阶的范围。建立了I-能控化控制器和脉冲模能控化控制器的参数表示式。由于上面的工作,基于PD状态反馈的脉冲消除问题可以通过两步完成。第一步设计I-能控化或脉冲模能控化控制器,第二步根据状态反馈消脉冲的方法求解比例增益。另外,对PD状态反馈脉冲消除还建立了能同时提供比例增益和导数增益的设计方法。以上所有的设计方法都是采用奇异值分解,因此提出的方法有较好的数值稳定性。
三、对正则广义系统提出了两大类观测器—比例积分观测器和比例积分导数观测器。基于一类Sylvester矩阵方程的显式参数化解给出这些观测器的参数化设计方法。提出的方法通过自由参数给出了所有观测器的增益矩阵的参数表达式。提出的方法能保证观测器系统是正则无脉冲的,且能提供所有的设计自由度。这些自由度能进一步参与优化满足系统额外限制并获得更好的系统性能。相比于文献中出现的PI观测器,本论文提出的广义PI观测器由于额外引入的观测器增益矩阵能提供更多的设计自由度,从而使系统获得更好的性能。
四、考虑了基于观测器的鲁棒控制问题。鲁棒性能由环路传递复现(LTR)性能表征。所涉及的观测器有Luenberger观测器,全维状态反测器,PI观测器,高阶比例积分观测器。基于复现误差的概念通过复现矩阵给出了精确LTR功能的充分必要条件。
五、考虑了柔性连接机器人系统基于PI观测器的状态反馈控制器的设计。结合提出的广义PI观测器的参数化方法和LTR条件根据设计自由参数建立控制器的LTR功能的性能指标。通过采用遗传优化算法给出了具有LTR功能的控制器的增益。通过与基于常规PI观测器的结果比较显示,广义PI观测器确实能够通过额外的自由度获得更好的LTR性能。
Descriptor-system models are more convenient and natural than normal systemsin the description of interconnected large-scale systems, mechanical multi-body mo-tion systems, or electrical networks. In addition, as an approach the model of descrip-tor linear systems has been utilized to develop robust stability condition and robustperformance index for some complex systems, such as time delay systems and neu-tral systems. Therefore, study on descriptor linear systems is both theoretically andpractically important.
A big difference between a descriptor linear system and a conventional linearsystem is that the response of a descriptor linear system may contain impulsive terms.Such infinite jumps are obviously destructive as they could completely destroy the sys-tem instantaneously. In addition, in practice the state of a system is usually not directlyavailable, so the state feedback control usually can not be realized directly. A feasiblemethod is to firstly asymptotically estimate the state vector by using an observer, andthen use the estimation of the state to construct the state feedback control. In orderto guarantee the accuracy of estimation, it is required that the designed observer sys-tem should be impulse free. Due to the above reasons, this dissertation systematicallyand deeply investigates the problem of impulse elimination and observer design. Thedetailed results are as follows.
1 Regularization via dynamic output feedback is investigated for square descriptorlinear systems. Necessary and sufficient conditions of regularizability via dy-namic output feedback are established. In addition, it is shown that the set of allregularizing gain matrix groups is a Zariski open set for regularizable systems.
2 The problems of impulse elimination via state feedback and proportional-derivative (PD) state feedback are dealt with. Based on a canonical equivalentform for descriptor linear systems, a general parametrization of all state feedbackgains which make the resulted closed-loop system impulse-free is presented. Inorder to deal with impulse elimination via PD state feedback, the concepts ofI-controllablizability and impulsive-mode controllablizability are introduced forsquare and nonsquare systems, respectively. Two class of criteria are given for the I-controllablizability and impulsive-mode controllablizability in terms of initialsystem matrices. General parametrization of all I-controllablizing and impulsive-mode controllablizing controllers are presented. With the above preparation, thesolution to impulse elimination via PD state feedback can be completed by atwo-step method.
3 Several types of observers are proposed for regular descriptor linear systems, andparametric design approach for these observers are established. The proposedobservers include generalized proportional-integral (PI) observers, proportional-multiple-integral (PMI) observers, generalized proportional-integral-derivative(PID) observers, proportional-multiple-integral-derivative (PMID)observers, andso on. The proposed approaches give parameterizations of all observer gain ma-trices in terms of some free parameters which represent the degrees of designfreedom, and can be further utilized to achieve additional specifications and per-formances. The proposed approach, which guarantees the regularity of the ob-server system, realizes the elimination of impulsive behaviors of the observersystem.
4 The problem of observer based robust control is investigated. The robustnessis characterized by the property of loop transfer recovery (LTR). The involvedobservers include Luenberger observers, full-order state observers, PI observersand PMI observers. Using the concept of recovery error, simple necessary andsufficient conditions for the controller are derived for exact LTR in terms of theso-called recovery matrices.
5 Generalized PI observer based state feedback controller is designed with thefunction of LTR for ?exible joint robots. By combining the proposed parametricexpression of observer gains and the recovery condition, an index is proposed tocharacterize the function of LTR. By adopting genetic optimization algorithm,controllers with LTR are provided. Compared with the results in the case ofPI observers, it is also shown that the extra freedom degrees of generalized PIobservers can provide better LTR performance.
引文
1 D. G. Luenberger. Dynamics equation in descriptor form. IEEE Transactions onAutomatic Control, 1977, 22:312-321
2 G. C. Verghese, B. C. Levy, T. Kailath. A generalized state-space for singularsystems. IEEE Transactions on Automatic Control, 1981, 26(4): 811-831
3 N. H. McClamroch. Singular systems of differential equations as dynamicalmodels for constrained robot systems. Proceedings of IEEE Robotics and Au-tomation Conference, San Francisco, CA, 1986, PP.21-28
4 E. Fridman, U. Shaked. A descriptor system approach to H∞control of lin-ear time-delay systems. IEEE Transactions on Automatic Control, 2002, 47(2):253-270
5 F. R. Gantmacher. The Theory of Matrices, Chelsea, New York, 1959
6 J. H. Wilkison. Linear differential equations and Kronecker’s canonical form.Recent Advances in Numerical Analysis (C. de Boor and G. H. Golub, Eds.),Academic, New York, 1978, pp. 231-265
7 G. Doetsch. Introduction to the Theory and Application of Laplace Transforma-tion. New York: Spring-Verlag, 1974
8 T. Geerts, V. Mehrmann. Linear differential equations with constant coeffi-cients: a distributional approach. Preprint 90-073, SFB 343, Univ. Bielefeld,Germany
9 T. Geerts. Solvability conditions, consistency, and weak consistent for lineardifferential-algebra equations and time-invariant singular systems: the generalcase. Linear Algebra and its Application, 1993, 181:111-130
10 D. Cobb. On solutions of linear differential equations with singular coefficients.J. Differential Equations, 1982, 46: 310-323
11 M. Malabre. Generalized linear systems: geometric and structural approaches.Linear Algebra and its Applications, 1989, 122/123/124: 591-621
12 Z. Zhou, M. A. Shayman, T. -J. Tarn. Singular systems: a new approach in thetime domain. IEEE Transactions on Automatic Control, 1987, 32: 42-50
13 M. Hou, A. C. Pugh, G. E. Hayton. A test for behavioral equivalence. IEEETransactions on Automatic Control, 2000, 45(11): 2177-2182
14 M. Hou, P. C. Muller. Causable observability of descriptor systems. IEEE Trans-actions on Automatic Control, 1999, 44(1): 158-163
15 Z. Yan, G. Duan. Time domain solution to descriptor variable systems. IEEETransactions on Automatic Control, 2005, 50(11): 1796-1799
16 E. L. Yip, R. Sincovec. Solvability, controllability and observability of continu-ous descriptor systems. IEEE Transactions on Automatic Control, 1981, 26(3):702-707
17 K. Ozcaladiran, F. L. Lewis. On the regularizability of singular systems. IEEETransactions on Automatic Control, 1990, 35(10): 1156-1160
18 C. Lin, J. Wang, C. B. Soh. Necessary and Sufficient conditions for the control-lability of linear interval descriptor systems. Automatica, 1998, 34(3): 363-367.
19 J. H. Chou, S. H. Chen, Q. L. Zhang. Robust controllability for linear uncertaindescriptor systems. Linear Algebra and its Applications, 2006, 414: 632-651
20何希勤,张大庆,张庆灵.广义区间动力系统的能控性.自动化学报, 2004,30(5): 763-771
21 B. Dziurla, R. W. Newcomb. Nonregular semistate systems: examples andinput-output pairing. Proceedings of the 26th Conference on Control and De-cision, Las Angeles, CA, 1987, pp.1125-1126
22 L. R. Fletcher. Regularizability of descriptor systems. Int. J. Syst. Sci, 1986, 47:843-847
23 V. Lovass-Nagy, D. L. Powers, R. J. Schilling. A note on controlling regular-izable linear time-invariant continuous-time descriptor system. J. Math. Syst.Estim. Contr., 1992, 2(3): 353-362
24 G. R. Duan. Eigenstructure assignment and response analysis in descriptor lin-ear systems with state feedback control. International Journal of Control, 1998,69(5): 663-964
25 A. Bunse-Gerstner, V. Mehrmann, N. K. Nichols. Regularization of descriptorsystems by derivative and proportional state feedback. SIAM J. Matrix Anal.Appl., 1992, 13(1): 46-67
26 V. Lovass-Nagy, D. L. Powers, R. J. Schilling. A note on regularizingdescriptor-variable systems by proportional-plus-derivative feedback. J. Math.Syst. Estim. Contr., 1994, 4: 341-351
27 L. R. Fletcher, J. Kautsky, N. K. Nichols. Eigenstructure assignment in descrip-tor systems. IEEE Transactions on Automatic Control, 1986, 31: 1138-1141
28 G. R. Duan, X. Zhang. Regularizability of linear descriptor systems via outputplus partial state derivative feedback. Asian Journal of Control, 2003, 5(3): 334-340
29 G. R. Duan, X. Zhang. Regularization of linear descriptor systems via outputplus partial state derivative feedback. Proceedings of the 5th Asia-Pacafic Con-ference on Control and Measurement, Yunnan, China, 2002, pp. 105-110
30 D. L. Chu, H. C. Chen, D. W. Ho. Regulariztion of singular systems by deriva-tive and proportional output feedback. SIAM J. Matrix Anal. Appl., Jan, 1998,19:21-38
31 A. Bunse-Gerstner, V. Mehrmann, N. K. Nichols. Feedback design for regular-izing of descriptor systems. Linear Algebra and its Applications, 1999, 29(1-3):119-151
32 V. Lovass-Nagy, D. L. Powers, R. J. Schilling. On regularizing descriptor sys-tems by output. IEEE Transactions on Automatic Control, 1994, 39(7): 1507-1509
33 V. Lovass-Nagy, D. L. Powers, R. J. Schilling. Addenda to”On regularizingdescriptor systems by output.”IEEE Transactions on Automatic Control, 1996,41(11): 1689-1690
34 D. L. Chu, D. W. C. Ho. Necessary and sufficient conditions for the outputfeedback regularization of descriptor systems. IEEE Transactions on AutomaticControl, 1999, 44(2): 405-412
35 A. Bunse-Gerstner, V. Mehrmann, N. K. Nichols. Regulariztion of singularsystems by output feedback. IEEE Transactions on Automatic Control, 1994,39(2): 1742-1748
36 D. L. Chu, D. Y. Cai. Regulariztion of singular systems by output feedback.Journal of Computational Mathematics, 2000, 18(1):43-60
37 D. Wang, C. B. Soh. On regularizing singular systems by decentralized outputfeedback. IEEE Transactions on Automatic Control, 1999, 44(1): 148-152
38 R. Yu. Regularizability of linear time-invariant descriptor systems under decen-tralized control. Automatica, 2005, 41: 1639-1644
39 H. H. Rosenbrock. Structural properties of linear dynamical systems. Interna-tional Journal of Control, 1974, 20:191-202
40 D. Cobb. Controllability, observability, and duality in singular systems. IEEETransactions on Automatic Control, 1984, 29(12): 1076-1082
41 Z. Yan. Geometric analysis of impulsive controllability for descriptor system.Systems and Control Letters, 2007, 56: 1-6
42 L. Pandolfi. Controllability and stabilization for linear system of the algebraicand differential equations. J. Optimiz. Theory Appl., 1980, 30: 601-620
43 F. L. Lewis. Descriptor systems: expanded descriptor equation and Markov pa-rameters. IEEE Transactions on Automatic Control, 1983, 28: 623-627
44 F. L. Lewis. Descriptor systems: fundamental matrix, reachability and observ-ability matrices, subspace. Proceedings of 23rd Conference on Control and De-cision, Las Vegas, NV, 1984, 28: 293-298
45 F. L. Lewis. Fundamental, reachability, and observability matrices for discretedescriptor systems. IEEE Transactions on Automatic Control, 1985, 30(5): 502-505
46 B. G. Mertzios, M. A. Christodoulou, B. L. Syrmos, F. L. Lewis. Direct Con-trollability and Observability Time Domain Conditions of Singular Systems.IEEE Transactions on Automatic Control, 1988, 33(8): 502-505
47 T. Yamada, D. G. Luenberger. Generic controllability theorems for descriptorsystems. IEEE Transactions on Automatic Control, 1985, 30(2): 144-152
48 T. Yamada, D. G. Luenberger. Algorithm to verify generic causality and control-lability of descriptor systems. IEEE Transactions on Automatic Control, 1985,30(9): 874-880
49 T. Aoki, S. Hosoe and S. Hayakawa. Structural controllability for linear systemin descriptor form. Trans. Soc. Instrum and Control Eng., 1983, 19(8): 628-635
50 K. J. Reinschke , G. Wiedemann. Digraph characterization of structural con-trollability for linear descriptor systems. Linear Algebra and its Applications,1997, 266:199-217
51 K. Ozcaldiran, D. W. Fountain, F. L. Lewis. Some generalized notations of ob-servability. IEEE Trans. Automat. Control, 1992, 37(9): 856-860
52 J. Y. Ishihara, M. H. Terra. Impulse controllability and observability of rect-angular descriptor systems. IEEE Transactions on Automatic Control, 2001,46(6): 991-994
53 M. Hou. Controllability, and elimination of impulsive in descriptor systems.IEEE Transactions on Automatic Control, 2004, 49(10): 1723-1727
54 J. Wei, W. Song. Controllability of singular systems with control delay. Auto-matica, 2001, 37: 1873-1877
55 G. Xie, L. Wang. Controllability of linear descriptor systems. IEEE Transac-tions on Circuits and Systems– I: Fundamental Theory and Applications, 2003,50(3): 455-460
56 C. Lin, J. L. Wang, G. H. Yang, C. B. Soh. Robust controllability and robustclosed-loop stability with static output feedback for a class of uncertain de-scritptor systems. Linear Algebra and its Applications, 1999, 297: 133-155
57 C. Lin, J. L. Wang, G. H. Yang, C. B. Soh. Robust C-controllability and/or C-observability for uncertain descriptor systems with interval perturbations in allmatrices. IEEE Transactions on Automatic Control, 1999, 44(9): 1768-1773
58 J. H. Chou, S. H. Chen, R. F. Fung. Sufficient conditions for the controllabilityof linear descriptor systems with both time-varying structured and unstructuredparameter uncertainties. IMA J. Math. Control Inform., 2001, 18(10): 469-477
59邹云,杨成梧.能控广义系统与不能控广义系统集之间的距离.自动化学报, 1991, 17(2): 220-224
60 Y. Y. Cao, Z. L. Lin. A descriptor system approach to robust stability analy-sis and controller synthesis. IEEE Transactions on Automatic Control, 2004,49(11): 2081-2084
61 T. Li, Y. Jia. Improved LMI representations for bounded real criterion of systemwith polytopic type uncertainty. Proceedings of the American Control Confer-ence, Denver, Colorado, 2003, pp.851-856
62 Q. H. Han. A descriptor system approach to robust stability of uncertain neutralsystems with discrete and distributed delays. Automatic, 2004, 40: 1791-1796
63 Y. Y. Wang, S. J. Shi and Z. J. Zhang. A descriptor-system approach to singularperturbation of linear systems. IEEE Transactions on Automatic Control, 1988,33(4): 370-373
64 L. Dai. Singular linear system. New York: Springer-Verlag, 1989
65 C. Lin, J. Wang, D. Wang, C. B. Sou. Robustness of uncertain descriptor sys-tems. Systems and Control Letters, 1997, 31: 129-138
66何希勤,柳萍,张大庆,张庆灵.广义区间动力系统脉冲模存在性判据.控制理论与应用, 2005, 22(5): 843-845
67 J. D. Cobb. Feedback and pole assignment in descriptor variable system. Inter-national Journal of Control, 1981, 33: 1135-1146
68 L. Dai. Impulsive modes and causality in singular systems. International Journalof Control, 1989, 50: 1267-1281
69 L. F. Lewis. A survey of linear singular systems. Circuits Syst., Signal. Proc.1986, 5:3-36
70 D. Cobb. Descriptor variable systems and optimal state regulation. IEEE Trans-actions on Automatic Control, 1983, 28(5): 601-611
71 G. R. Duan, X. Zhang. Dynamical Order Assignment in Linear Descriptor Sys-tems via Partial State Derivative Feedback. Annual Conference of the UK-ChinaAutomation Society, Beijing, China, 2002
72 G. R. Duan, X. Zhang. Dynamical order assignment in linear descriptor sys-tems via state derivative feedback. Proceedings of the 41th IEEE Conferenceon Decision and Control, vol. 4, pp. 4533-4538, Las Vegas, USA, 2002
73 G. R. Duan. Eigenstructure assignment in descriptor systems via output feed-back: a new complete parametric approach. International Journal of Control,1999, 72(4): 345-364
74 S. Y. Zhang. Pole placement for singular systems. System and Control Letters,1989, 12: 339-346
75 D. W. Wang, C. B. Soh. Rank of matrix pencils at infinity and its applicationsin descriptor systems. Proceedings of the American Control Conference, Albu-querque, New Mexico Jun, 1997, pp. 2583-2584
76 R. Yu, D. Wang. Structured properties and poles assignment of LTI singularsystems under output feedback. Automactica, 2003, 39: 685-692
77 R. Yu, D. Wang. On impulsive modes of linear singular systems subject to de-centralized output feedback. IEEE Transactions on Automatic Control, 2003,48(10): 1804-1809
78 R. Yu. On impulsive algebraic multiplicities of linear time-invariant singularsystems under feedback. Automatica, 2005, 41: 1657-1662
79 W. Q. Liu, K. L. Teo, W. Y. Yan. Optimal simultaneous stability of descriptorsystems via output feedback. International Journal of Control, 1996, 64: 595-613
80 W. Q. Liu, W. Y. Yan, K. L. Teo. On initial instantaneous jumps of singularsystems. IEEE Transactions on Automatic Control, 1995, 40(9): 1650-1655
81 J. L. Lin, S. J. Chen. Robustness analysis of uncertain linear singular systemswith output feedback control. IEEE Transactions on Automatica Control, 1999, 44(10): 1924-1929
82 D. Wang, P. Bao. Robust impulse control of uncertain singular systems by de-centralized output feedback. IEEE Transactions on Automatica Control, 2000, 45(1): 795-800
83 D. G. Luenberger. An introduction to observers. IEEE Transactions on Auto-matic Control, 1971, 16(6): 596-602
84 M. El-Tohami, V. Lovass-Nagy, R. Mukundan. On the design of observers forgeneralized state space systems using singular value decomposition. Interna-tional Journal of Control, 1983, 38(3): 673-685
85 M. Verhaegen, P. Van Dooren. A reduced observer for descriptor systems. Sys-tems and Control Letters, 1986, 8(11):29-38
86 B. Shafai, R. L. Corroll. Design of a minimal-order observer for singular sys-tem. International Journal of Control, 1987, 45(3): 1075-1082
87 M. M. Fahm, J. O’Reilly. Observer for descriptor systems. International Journalof Control, 1989, 49(6): 2013-2028
88 L. Dai. Observers for discrete singular systems. IEEE Transanctions on Auto-matic Control, 1988, 33(2): 187-191
89 L. F. Lewis. Geometric design technique for observers in singular systems. Au-tomatica, 1990, 26: 411-415
90 P. C. Muller, M. Hou. On the observer design for descriptor systems. IEEETransactions on Automatic Control, 1991, 40(1): 133-136
91 V. Syrmos. Observer design for descriptor systems with unmearable distur-bances. Proceedings of the 30th Conference on Decision and Control, England,1992, pp. 981-982
92张国山,柴天佑,顾兴源.一般动态系统讲阶观测器的设计及参数化表示.控制理论与应用, 1997, 14(4):584-588
93 J. Carvalho, B. Datta. An algorithm for generalized Sylvester-observer equationfor state estimation of descriptor systems. Proceedings of the 30th Conferenceon Decision and Control, Las Vegas, 2002, pp. 3021-3026
94 M. Darouach, M. Boutayeb. Design of observers for descriptor systems. IEEETransactions on Automatic Control, 1995, 40(7): 1323-1327
95 B. Wojciechowski. Analysis and synthesis of proportional-integral observersfor single-input-single-output time-invariant continuous systems. PhD thesis,Gliwice, Poland, 1978
96 T. Kaczorek. Proportional-integral observers for linear multivariable tiem-varying systems. Regelungstechnik, 1979, 27: 359-362
97 B. Shafai, R. L. Carroll. Design of proportional integral observer for linear time-varying multivariable systems. Proceedings of 24th IEEE conference on Deci-sion and Control, Ft. Lauderdale, FL, 1985, pp.597-599
98 S. Beale, B. Shafai. Robust control system design with a proportional integralobserver. International Journal of Control, 1989, 50:97-111
99 K. B. Krishna, K. Pousga. On the design of integral and proportional inte-gral observers. Proceedings of the American Control Conference,Chicago,2000,pp.3725-3729
100 D. Soker, T. Yu, P. C. Müller. State estimation of dynamical systems with non-linearities by using proportional-integral observer. International Journal of Sys-tems Science, 1995, 26:1571-1582
101 B. Shafai, C. T. Pi, S. Nork. Simultaneous Disturbance attenuation and faultdetection using proportional integral observers. Proceedings of the AmericanControl Conference, Anchorage, 2002, pp.1647-1649
102 H. H. Niemann, J. Stoustrup, B. Shafai, S. Beale. LTR design of proportional-integral observers. Int. J. Robust Nonlinear Control, 1995, (5): 671-693
103 Y. X. Yao, Y. M. Zhang, R. Kovacevic. Loop transfer recovery design withproportional integral observer based on H∞optimal observation. Proceedingsof the American Control Conference, New Mexico, 1997 , 1:786-790
104 B. Shafai, S. Beale, J. Sroustrup. LTR design of discrete-time proportional-integral observers. IEEE Transactions on Automatic Control, 1996, 41(7):1056-1062
105 G. R. Duan, G. P. Liu, S. Thompson. Eigenstructure assignment design forproportional-integral observers—The continuous-time case. IEE ProceedingsControl Theory and Application, 2001, 148(3): 263-267
106 G. P. Jiang, S. P. Wang, W. Z. Song. Design of observer with integrators for lin-ear systems with unknown input disturbances. Electron. Lett., 2000, 36: 1168-1169
107蒋国平,宋文忠.具有未知输入干扰的离散状态估计器设计.控制理论与应用, 1998, 15(4): 507-514
108 H. S. Kim, T. K. Yeu, S. Kawaji. Design of PI observers for descriptor linearsystems. Transactions on Control, Automation and Systems Engeering, 1997,3(4): 332-337
109 H. S. Kim, S. B. Kim, S. Kawaji. Fault detection in linear descriptor systems viaunknown input PI observer. Transactions on Control, Automation and SystemsEngeering, 2001, 3(2):77-82
110 G. R. Duan. Solution to matrix equation AV +BW = EV F and eigenstructureassignment for descriptor linear systems. Automatica, 1992, 28(3): 639-643
111 G. R. Duan. On the solution to Sylvester matrix equation AV + BW = EV F.IEEE Transactions on Automatic Control, 1996, 41(4): 2490-2494
112 Z. Gao, D. W. C. Ho. Proportional multiple-integral observer design for descrip-tor linear systmes with measurement output disturbances. IEE Proc.-ControlTheory Appl., 2004, 151(3): 279-288
113 D. Koening. Unknown input proporitional multiple-integral observer design forlinear descriptor systems: application to state and fault estimation. IEEE Trans-actions on Automatica Control, 2005, 50(2): 212-217
114 Z. Gao. PD observer parameterization design for descriptor systems. Journal ofFranklin Institute, 2005, 342:551-564
115 M. Hou, P. C. Muller. Observer design for descriptor systems. IEEE Transac-tions on Automatica Control, 1999, 44(1): 164-168
116 W. Wang, Y, Zou. Analysis of impulsive modes and Luenberger observers fordescriptor systems. Systems Control Letters, 2001, 44: 347-353
117 R. Nikoukhah, S. L. Campbell aF. Delebecque. Observer design for generallinear time-invariant system. Automatica, 1998, 34(5): 575-583
118 M. El-Tohami, V. Lovass-Nagy. On input function observers for generalizedstate-space systems. International Journal of Control, 1984, 40(5): 903-922
119 Y. Park, J. L. Stein. Closed-loop, state and inputs observer for systems withunkwown input. International Journal of Control, 1988, 48(5): 1121-1136
120 M. Hou, R. J. Patton. Input observability and input reconstruction. Automatica,1998, 34(6): 789-794
121 C. Edwards, S. K. Spurgeon, R. J. Patton. Sliding mode observers for faultdetection and isolation. Automatica, 2000, 36: 541-553
122 C. P. Tan, C. Edwards. Sliding mode observers for detection and reconstructionof sensor faults. Automatica, 2002, 38: 1815-1821
123 S. Zhou, L. Sun, Z. Cheng. Input estimation for uncertain linear singular sys-tems and robust stabilization. Proceedings of Conference on Decision and Con-trol, 2001, 2856-2857
124 S. Zhou, L. Sun, Z. Cheng. Observer design for discrete-time descriptor sys-tems with unknown and inputs estimation. Proceedings of the 5th Asian ControlConference, 2004, 804-808
125 C. W. Yang, H. L. Tan. Observer design for singular systems with unknowninputs. Intertional Journal of Control, 1989, 49(6): 1937-1946
126 P. N. Paraskevopoulos, F. N. Koumboulis, K. G. Tzierakis, G. E. Panagiotakis.Observers design for generalized state space systems with unknown input. Syst.Contr. Letter, 1992, 18:309-321
127 M. Darouach, M. Zasadzinski, M. Hayar. Reduced-order observer design for de-scriptor systems with unknown inputs. IEEE Transactions on Automatica Con-trol, 1996, 41(7): 1068-1072
128 S. Kawaji, K. Sawada. Observer design for linear descriptor systems with un-known inputs. IECON’91, 2285-2288
129 S. F. Lin, A. P. Wang. Unknown input observers for singular systems designedby eigenstructure assignment. J. of Franklin Inst., 2003, 340: 43-61
130 Koening, S. Mammar. Design of proportional-integral observer for unknown in-put descriptor systems. IEEE Transactions on Automatic Control, 2002,47(12):2057-2062
131 M. Hou. Fault detection and isolation for descriptor systems. In Issues of FaultDiagnosis for Dynamic Systems, Berlin: Springer, pp.115-144
132 T. K. Yeu, S. Kawaji. Fault detection and isolation for descriptor systems usingsliding mode observer. Proceedings of Conference on Decision and Control,2001, 596-597
133 T. K. Yeu, S. Kawaji. Sliding modes observer based fault detection and isolationin descriptor linear systems. Proceedings of the American Control Conference,Anchorage, 2002, 4543-4548
134 G. R. Duan, D. Howe, R. J. Patton. Robust fault detection in descriptor lin-ear systems via generalized unknown input observers. International Journal ofSystems Science, 2002, 33(5): 369-377
135 G. R. Duan. Eigenstructure assignment and response analysis in descriptor sys-tems with state feedback control. International Journal of Control, 1998, 69(5):663-694
136 J. C. Doyle, G. Stein. Robustness with observers. IEEE Transactions on Auto-matic Control, Aug. 1979, AC-24(4): 607-611
137 J. M. Maciejowski. Asymptotic recovery for discrete-time systems. IEEE Trans-actions on Automatic Control, June 1985, AC-30(4): 602-605
138 T. Ishihara, H. Takeda. Loop transfer recovery techniques for discrete-time op-timal regulator using prediction estimators. IEEE Transactions on AutomaticControl, Dec. 1986, AC-31(12): 1149-1151
139 G. Stein, M. Athans. The LQG/LTR procedure for multivariable feedback con-trol design. IEEE Transactions on Automatic Control, Feb. 1987, AC-32(2):105-114
140 J. B. Moore, L. Xia. Loop recovery and robut state estimate feedback designs.IEEE Transactions on Automatic Control, June 1987, AC-32(6): 512-517
141 A. Saberi, P. Sannuti. Observer design for loop transfer recovery and for uncer-tain dynamical systems. IEEE Transactions on Automatic Control, Aug. 1990,35(8): 878-897
142 Z. Zhang, J. S. Freudenberg. Loop transfer recovery for nonminimum phaseplants. IEEE Transactions on Automatic Control, May 1990, 35(5): 547-553
143 B. A. L. de la Barra. Frenquency domain tradeoffs in loop transfer recovery formultivariable nonminimum phase discrete-time systems. IEEE Transactions onAutomatic Control, July 1994, 39(7): 574-577
144 M. Tadjine, M. M’Saad, L. Dugard. Discrete-time compensators with looptransfer recovery. IEEE Transactions on Automatic Control, June 1994, 39(6):1259-1262
145 L. Turan, D. L. Mingori, G. C. Goodwin. Loop transfer recovery design us-ing biased and unbiased controllers. IEEE Transactions on Automatic Control,March 1994, 39(3): 601-605
146 L. Turan, D. L. Mingori. A unified loop transfer recovery approach to robustcontrol using H∞optimization methods. Automatica, July 1995, 31(7): 1045-1052
147 M. Fu. Exact, optimal, and partial loop transfer recovery. Proceedings of the 29th Conference on Decision and Control, Hawaii, Dec. 1990, pp. 1841-1846
148 P. Sφgaard-Andersen. Loop transfer recovery with minimal-order observers.Proceedings of the 28th Conference on Decision and Control, Los Angeles,1987, pp.933-938
149 S. Beale, B. Shafai. Loop transfer recovery via a proportional integral observer.IEEE International Conference on Systems Engineering, Aug. 1990, pp. 468-473
150 B. Shafai, L. H. Keel, S. Beale. Zero assignment and loop transfer recoveryin LQG design. Proceedings of the 29th Conference on Decision and Control,Hawaii, Dec. 1990, pp. 1217-1221
151 H. H. Niemann, P. Sφgaard-Andersen, J. Stoustrup. Loop transfer recovery forgeneral observer architectures. International Journal of Control, 1991, 53(5):1177-1203
152 M. S. Chen, C. H. Chen, F. Y. Yang. An LTR-observer-based dynamic slidingmode control for chattering reduction. Automatica, 2007, 43(6): 1111-1116
153 W. Fulton. Algebraic topology: A first course. Berlin: Springer, 1995
154 T. J. Owens, S. Askarpour. Integrated approach to to eigenstructure assignmentin descriptor systems by PD and P state feedback. IEE Proc.-Control TheoryAppl., 2000, 147: 407-415
155 D. L. Chu, H. C. Chan, D. W. C. Ho. A general framework for state feedbackpole assignment of singular systems. International Journal of Control, 1997, 67: 135-152
156 G. R. Duan. Parametric eigenstructure assignment via output feedback based onsingular value decompositions. IEE Proc.-Control Theory Appl., 2003, 150(1): 93-100
157 F. L. Lewis, K. Ozcaldiran. Geometric structure and feedback in singular sys-tems. IEEE Transactions on Automatic Control, 1989, 34: 459-455
158 B. G. Mertzios. Leverrier’s algorithm for singular systems. IEEE Transactionson Automatic Control, 1984,29(7): 652-653
159 G. C. Goodman. The LQG/LTR method and discrete-time control systems. M.I. T., Cambridge, MA, Tech. Rep. LIDS-TH-1392, 1984
160 A. Ailon. Asymptotic stability in a ?exible-joint robot with model uncertaintyand muptiple time delays in feedback. Journal of the Franklin Institute, 2004, 341: 519-531
161 M. W. Spong. Modeling and control of elastic joint robots. Journal of DynamicSystems, Measurement and Control, 1987, 109: 310-319
162 S. Gogate, Y. Lin. Formulation and control of robots with link and joint ?exi-bility. Robotica, 1993, 11: 273-282
163 S. Raghavar, J. K. Hedrick. Observer design for a class of nonlinear systems.International Journal of Control, 1994, 59: 2-10
164 D. N. Shields. Observer design and detection for nonlinear descriptor systems.International Journal of Control, 1997, 67(2): 153-168