基于耗散系统原理的非线性系统鲁棒镇定和镇定问题研究
|
摘要
最近一段时期，基于耗散系统原理的非线性系统鲁棒镇定和镇定设计取得了许多重要成果，但仍然有待深入。本论文一方面给出相关理论结果的补充和改进，另一方面，运用已有的和新发展的理论结果给出复杂系统的鲁棒镇定和镇定设计。具体地说，本论文的研究内容如下：
1．无源性原理是耗散性原理的重要组成部分，我们探讨了该原理在鲁棒镇定和镇定设计中的应用。运用仿射无源系统的Kalman-Yacubovitch-Popov引理，饱和镇定非仿射非线性系统；运用联级无源系统的稳定原理鲁棒镇定几类不确定系统；运用零状态可探测概念，给出了镇定从驱动系统相对较弱的充分条件。
2．输入到状态稳定原理是耗散系统原理的新近发展，我们对其进行理论补充并探讨新结论的应用。给出了输入到状态稳定的一个新刻画，该结论可以为工程中输入到状态镇定设计提供理论依据；总结了一个简单实用的非线性小增益原理，与此结合，使输入到状态稳定原理成为镇定设计的一种更为有效的分析工具。
3．探讨无源性原理在输入到状态镇定中的应用。借助零状态可探测概念，减弱了通常文献中所需的前提条件，在此基础上研究了一类输入饱和线性系统的输入到状态镇定。
4．探讨控制李雅普诺夫函数在鲁棒镇定和镇定设计中的关键性作用。基于控制李雅普诺夫函数的Sontag-Type控制，是仿射系统鲁棒镇定研究中一种非常重要的控制律，通过研究我们发现，该控制律实质上是一种变结构控制；基于这一认识，也考虑到控制李雅普诺夫函数难于构造，我们抽象出弱控制李雅普诺夫函数概念，并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的镇定作用和优化特性；借鉴控制李雅普诺夫函数的抽象方式以及Sontag-Type控制的特殊结构，探讨了一类受扰系统的耗散化控制；探讨了齐性度理论与控制李雅普诺夫函数相结合的镇定设计问题。
5．探讨弱李雅普诺夫函数在镇定设计中的作用。刻画一类存在半正定弱李雅普诺夫函数的全局渐近稳定系统，并用所得结果改进了李雅普诺夫递推设计的一个重要理论依据；如何由弱李雅普诺夫函数重构控制李雅普诺夫函数，是一个十分重要的问题，因为成功的重构意味着可以进行深入的鲁棒分
产
摘要
析与设计，针对仿射系统我们给出了可以重构的充分条件，并用典型例子说
明了构造过程.
6.在有限场(p全1)增益稳定基础上发展起来的非线性枷控制研究方兴未艾，
我们作出了一点理论方面的探讨，给出了一个不同于微分对策的估计最佳
控制和最糟扰动的不等式方法.
For recent years, although a great many important results have been achieved in the field of robust stabilization and stabilization design of nonlinear systems based on dissipative system theory, many researches remain to be done. In this dissertation, on the one hand, we reinforce or improve some theoretic results, on the other hand, by using theorems existed or developed in this dissertation, we pursue the researches on robust stabilization and stabilization design in diverse complex nonlinear systems. The contributions of this dissertation consist of the following:
1.Passivity theory is an important component of dissipative system theory, we investigate its applications to robust stabilization and stabilization design. Non-affine nonlinear systems via bounded controls and Kalman-Yakubovitch -Popov lemma of affine passive systems are stabilized. Several kinds of nonlinear systems with uncertainty by using stability theory of cascaded passive systems are stabilized robustly. The relative weaker sufficient conditions of stabilizing a class of driven-driving systems by using the concept of zero-state-detectability are put forward.
2.1nput-to-state stable theory is a new area of dissipative system theory, we propose some theoretic results and investigate their applications. A new characterization of input-to-state stability which is beneficial to input-to-state stabilization design is presented. A nonlinear small-gain theory with which input-to-state stable theory becomes a more effective analysis tool of stabilization design is put forward.
3.We investigate the function of passivity theory in input-to-state stabilization. The usual precondition guaranteeing input-to-state stabilization by exploiting the concept of zero-state-detectability is weakened, and a class of linear systems subject to saturation by using the results above is input-to-state stabilized. 4.The decisive function of control Lyapunov functions in robust stabilization and stabilization design is studied. Since Sontag-Type control based on control
Lyapunov function is an important control law in robust stabilization of affine systems, we point out that is a kind of variable structural control in essence. Due to this recognition and the fact that control Lyapunov functions are difficult to be constructed, we propose the concept of weak control Lyapunov function and then prove the stabilizing property and the robustness of Sontag-Type control. Using the way of proposing the control Lyapunov function and the special structure of Sontag-Type control, we investigate the dissipassivation control of a kind of perturbed nonlinear systems. The applications of homogeneity theory to stabilization design based on control Lyapunov functions are studied and some new results are obtained.
5.The function of weak Lyapunov functions in stabilization design is studied. We characterize a kind of globally asymptotically stable systems which have only semi-definite positive weak Lyapunov function. Based on this characterization, we improve the theoretic result which is the foundation of Lyapunov backstepping design. The problem that how to construct a control Lyapunov function from a weak Lyapunov function is a significant one, because the successful reconstruction implies that robust analysis and design can be probed in depth. For affine nonlinear systems, we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples.
6.Nonlinear H-infinite control based on Lp(p l) gain stability is being extensively investigated recently. We present a theoretic result, i.e., put forward an inequality approach, which is different from the usual differential game method, to estimate the best control and the worst disturbance.
1．无源性原理是耗散性原理的重要组成部分，我们探讨了该原理在鲁棒镇定和镇定设计中的应用。运用仿射无源系统的Kalman-Yacubovitch-Popov引理，饱和镇定非仿射非线性系统；运用联级无源系统的稳定原理鲁棒镇定几类不确定系统；运用零状态可探测概念，给出了镇定从驱动系统相对较弱的充分条件。
2．输入到状态稳定原理是耗散系统原理的新近发展，我们对其进行理论补充并探讨新结论的应用。给出了输入到状态稳定的一个新刻画，该结论可以为工程中输入到状态镇定设计提供理论依据；总结了一个简单实用的非线性小增益原理，与此结合，使输入到状态稳定原理成为镇定设计的一种更为有效的分析工具。
3．探讨无源性原理在输入到状态镇定中的应用。借助零状态可探测概念，减弱了通常文献中所需的前提条件，在此基础上研究了一类输入饱和线性系统的输入到状态镇定。
4．探讨控制李雅普诺夫函数在鲁棒镇定和镇定设计中的关键性作用。基于控制李雅普诺夫函数的Sontag-Type控制，是仿射系统鲁棒镇定研究中一种非常重要的控制律，通过研究我们发现，该控制律实质上是一种变结构控制；基于这一认识，也考虑到控制李雅普诺夫函数难于构造，我们抽象出弱控制李雅普诺夫函数概念，并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的镇定作用和优化特性；借鉴控制李雅普诺夫函数的抽象方式以及Sontag-Type控制的特殊结构，探讨了一类受扰系统的耗散化控制；探讨了齐性度理论与控制李雅普诺夫函数相结合的镇定设计问题。
5．探讨弱李雅普诺夫函数在镇定设计中的作用。刻画一类存在半正定弱李雅普诺夫函数的全局渐近稳定系统，并用所得结果改进了李雅普诺夫递推设计的一个重要理论依据；如何由弱李雅普诺夫函数重构控制李雅普诺夫函数，是一个十分重要的问题，因为成功的重构意味着可以进行深入的鲁棒分
产
摘要
析与设计，针对仿射系统我们给出了可以重构的充分条件，并用典型例子说
明了构造过程.
6.在有限场(p全1)增益稳定基础上发展起来的非线性枷控制研究方兴未艾，
我们作出了一点理论方面的探讨，给出了一个不同于微分对策的估计最佳
控制和最糟扰动的不等式方法.
For recent years, although a great many important results have been achieved in the field of robust stabilization and stabilization design of nonlinear systems based on dissipative system theory, many researches remain to be done. In this dissertation, on the one hand, we reinforce or improve some theoretic results, on the other hand, by using theorems existed or developed in this dissertation, we pursue the researches on robust stabilization and stabilization design in diverse complex nonlinear systems. The contributions of this dissertation consist of the following:
1.Passivity theory is an important component of dissipative system theory, we investigate its applications to robust stabilization and stabilization design. Non-affine nonlinear systems via bounded controls and Kalman-Yakubovitch -Popov lemma of affine passive systems are stabilized. Several kinds of nonlinear systems with uncertainty by using stability theory of cascaded passive systems are stabilized robustly. The relative weaker sufficient conditions of stabilizing a class of driven-driving systems by using the concept of zero-state-detectability are put forward.
2.1nput-to-state stable theory is a new area of dissipative system theory, we propose some theoretic results and investigate their applications. A new characterization of input-to-state stability which is beneficial to input-to-state stabilization design is presented. A nonlinear small-gain theory with which input-to-state stable theory becomes a more effective analysis tool of stabilization design is put forward.
3.We investigate the function of passivity theory in input-to-state stabilization. The usual precondition guaranteeing input-to-state stabilization by exploiting the concept of zero-state-detectability is weakened, and a class of linear systems subject to saturation by using the results above is input-to-state stabilized. 4.The decisive function of control Lyapunov functions in robust stabilization and stabilization design is studied. Since Sontag-Type control based on control
Lyapunov function is an important control law in robust stabilization of affine systems, we point out that is a kind of variable structural control in essence. Due to this recognition and the fact that control Lyapunov functions are difficult to be constructed, we propose the concept of weak control Lyapunov function and then prove the stabilizing property and the robustness of Sontag-Type control. Using the way of proposing the control Lyapunov function and the special structure of Sontag-Type control, we investigate the dissipassivation control of a kind of perturbed nonlinear systems. The applications of homogeneity theory to stabilization design based on control Lyapunov functions are studied and some new results are obtained.
5.The function of weak Lyapunov functions in stabilization design is studied. We characterize a kind of globally asymptotically stable systems which have only semi-definite positive weak Lyapunov function. Based on this characterization, we improve the theoretic result which is the foundation of Lyapunov backstepping design. The problem that how to construct a control Lyapunov function from a weak Lyapunov function is a significant one, because the successful reconstruction implies that robust analysis and design can be probed in depth. For affine nonlinear systems, we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples.
6.Nonlinear H-infinite control based on Lp(p l) gain stability is being extensively investigated recently. We present a theoretic result, i.e., put forward an inequality approach, which is different from the usual differential game method, to estimate the best control and the worst disturbance.
引文
1． Report on the workshop:'Challenges to control:A collective view'.IEEE Trans.Autom.Contr.,1986,32(4) :275-285
2． Willems J C.Dissipative dynamical systems.Part Two:linear systems with quadratic supply rates.Arch.Rat.Mech.Anal.,1972,45:352-393
3． Hill D J.Moylan P J.The stability of nonlinear dissipative systems.IEEE Trans.Autom.Contr.,1976,2:708-711
4． Byrnes C I,Isidori A.Willems J C.Passivity,feedback equivalence and the global stabilization of minimum phase nonlinear systems.IEEE Trans.Autom.Contr.,1991,36:1228-1240
5． Sepulchre R,Jankovic M,Kokotovic P V.Constructive nonlinear control.London:Springer,1997
6． Isidori A,Joshi S M,Kelkar A G Asymptotic stability of interconnected passive nonlinear systems.Int.J.Robust Nonlinear Control,1999(9) :261-273
7． Byrnes C I,Martin C F.An integral-invariance principle for nonlinear systems.IEEE Trans.Automatic Control,1995,40:983-993
8． Lin W.Global asymptotic Stabilization of general Nonlinear Systems with stable Free Dynamics via passivity and bounded feedback.Automatica,1996,32(6) :915-924
9． Ortega R.Passivity properties for stabiliztion of cascaded nonlinear systems.Automatica,1991,27(2) :423-424
10． Lin W,Shen T.Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty.Automatica,1999,35:35-47
11． 申铁龙．机器人鲁棒控制基础．北京：清华大学出版社，2000：66-77
12． Mei Shenwei,Shen T.Sun Y,Lu Q.Passivation control of nonlinear systems with disturbances.Control Theory and Applications,1999,16(6) :797-801
13． Teel A R,Praly L.On assigning the derivative of disturbance attenuation control Lyapunov function.MCSS,2000,3:95-124
14． Jiang Z P,Hill D J.Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems.IEEE Trans.Automat.Contr.,1998,43(7) :992-997
15． Isidori A,Astolfi A.Disturbance attenuation and H-infinite control via measurement feed-back in nonlinear systems.IEEE Trans.Automatic Control,1992(37) :1283-1293
16． A J van der Schaft.L2-gain and passivity techniques in nonlinear control.2nd ed.Lecture Notes in Control and Information Sciences.vol 218． Springer:Berlin,1996
17． Sontag E D.Smooth stabilization implies coprime factorization.IEEE Trans.Automa.Contr.,1989,34(4) :435-443
18． Sontag E D,Wang Y.On characterizations of the input-to-state stability property.Syst.Contr.Lett.,1995,24:351-359
19． Jiang Z P,Teel A R,Praly L.Small-gain theorem for ISS systems and applications.MCSS,1994(7) :95-120
20． Krstic M,Li Z.Inverse optimal design of input-to-state stabilizing nonlinear controllers.IEEE Trans.Automatic Control,1998,43:336-349
21． Jiang Z P,Mareels I M and Wang Y.A Liapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems.Automatica,1996,32(8) :1211-1215
22． Arack M.Seron M,Bravsky J,Kokotovic P.Robustification of backstepping against input unmodeled dynamics.IEEE Trans.Automa.Contr.,2000,45(8) :1-6
23． Sontag E D.A universal construction of Artstein's theorem on nonlinear stabilization.Syst.Contr.Lett.,1989,13:117-123
24． Moylan P J.Implications of passivity in a class of nonlinear systems.IEEE Trans.Automa.Contr,1974,18:373-381．
25． Pomet J B.Explicit design of time varying stabilizing control laws for a class of controllable systems without drift.Syst.Contr.Lett.,1992,18:147-158
26． Bensoubaya M,Ferfera A,Iggidr A.A Jurdjevic-Quinn type theorem for nonlinear systems.In Proc.37th IEEE CDC,December,1998:2485-2490
27． Mazenc F,Praly L.Adding integrators,saturated controls and stabilization for feedforward systems.IEEE Trans.Autom.Contr.,1996,41(11) :1559-1578
28． Brogliato B,Laudau I,Lozano R.Adaptive motion control of robot manipulators:a unified approah based on passivity.Int J Robust and Nonlinear control,1991,1:187-202
29． Lu Weiming,Packard A.Adaptive H-infinite control for nonlinear systems:a dissipation theor-etical approach.Caltech CDS Tech.Memo.,No.CIT-CDS-96-019,1996．
30． Luenberger D G.Optimization by vector space metods.New Ydrk:John Wiley & Sons,Inc.,1969
31． Marino R,Tomei P.Observer-based adaptive stabilization for a class of nonlinear systems. Automatica,1992,28:787-793
32． Sontag E D.Further facts on input to state stabilization.IEEE Trans.Automa.Contr.,1990,35(4) :437-442
33． Sontag E D.Teel A.Changing supply functions in input/state stable systems,IEEE Trans.Autom.Contr.,1995,40:1476-1478
34． Sontag E D.Wang Y.A notion of input-to-output stability.In Proc.European Control Conf.,Brussel,July,1997
35． Angeli D.Input-to-state stability of PD-controlled robotic systems.Automatica,1999,35:1285-1290
36． Liu W.Chitour Y,Sontag E D.On finite-gain stabilizability of linear systems subject to input saturation.SIAM J Control and Optimization,1996,34(4) :1190-1219
37． Teel A R.A nonlinear small gain theorem for the analysis of control systems with saturation.IEEE Trans.Automa.Contr.,1996,41(9) :1256-1270
38． Byrnes C I,Isidori A.New results and examples in nonlinear feedback stabilization.Syst.Contr.Lett.,1989,12:437-442．
39． Sussmann H J,Sontag E D,Yang Y.A General Result on the Stabilization of Linear Systems Using Bounded Controls.EEEE Trans.Automat.Contr.,1994,39:2411-2425
40． Artstein Z.Stabilization with relaxed controls.Nonlinear analysis,1983,7:1163-1173
41． Clarke F H,Ledyaeve Y S,Sontag E D,Subbotin A I.Asymptotic controllability implies feedback stabilization.IEEE Trans.Autom.Contr.,1997,42:1394-1407
42． Bacciotti A.Local stabilizability of nonlinear control systems.Series on advances in mathema-tics for applied sciences,World Scientific,1992
43． 高为炳．变结构控制理论基础．北京：中国科学出版社，1990
44． Qin Huashu,Hong Yiguang.Passivity.stability and optimality.Control Theory and Applica-tions,1994,11 (4) :421-427
45． Shiriaev A S.The Notion of V-detectability and Stabilization of Invariant Sets of Nonlinear Systems.Proceedings of the 37 IEEE Conference on Decision & Control,Tempa,Florida,USA,1998
46． Glad S T.Robustness of Nonlinear State Feedback-A Survey.Automatica,1987,23:425-435
47． Krstic M.Kanellakopoulos I,Kokotovic P.Nonlinear and adaptive control design.New York:Wiley,1995
48． Sontag E D.Mathematical control theory-deterministic finite dimensional syste-ms.New York:Springer-Verlag,1990
49． Vidyasagar M.Decomposition techniquues for large-scare systems with non-additive interac-tions:stability and stabilizability.IEEE Trans.Automat.Control,1980(25) :773-779
50． Andriano V,Bacciotti A,Beccari G.Global stability and external stability of dynamic systems.Nonlinear Analysis,1997(28) :1167-1185
51． Iggidr A.kalitine B.Outbib R.Semi-definite Lyapunov functions.stability and stabilization.MCSS,1996,9:95-106
52． Carr J.Applications of center manifold theory.New York:Springer-Verlag,1981
53． Faubourg L.Pomet J B.Strict control Lyapunov functions for homogeneous Jurdjevic-Quinn type systems.In Nonlinear Control Systems Design Symphosium,IFAC,1998:823-829
54． Morin P.Robust stabilization of the angular velocity of a rigid body with two actuators.European J of Control,1996,2(1) :51-56
55． Doyle J C.Glover K,Khagonekar P.Francis B A.State-space solution to standard H2 and H-infinite control problem.IEEE Trans.Automatic Control,1989,34:831-842
56． Ball J A,Kachroo P,Krener J A.H-infinite tracking control for a class of nonlinear systems.IEEE Trans.Autom.Contr.,1999,44(6) :1202-1206
57． Isidori A,Byrnes C I.Optimal regulation of nonlinear systems.IEEE Trans.Autom.Contr.1990,35(2) :131-140
2． Willems J C.Dissipative dynamical systems.Part Two:linear systems with quadratic supply rates.Arch.Rat.Mech.Anal.,1972,45:352-393
3． Hill D J.Moylan P J.The stability of nonlinear dissipative systems.IEEE Trans.Autom.Contr.,1976,2:708-711
4． Byrnes C I,Isidori A.Willems J C.Passivity,feedback equivalence and the global stabilization of minimum phase nonlinear systems.IEEE Trans.Autom.Contr.,1991,36:1228-1240
5． Sepulchre R,Jankovic M,Kokotovic P V.Constructive nonlinear control.London:Springer,1997
6． Isidori A,Joshi S M,Kelkar A G Asymptotic stability of interconnected passive nonlinear systems.Int.J.Robust Nonlinear Control,1999(9) :261-273
7． Byrnes C I,Martin C F.An integral-invariance principle for nonlinear systems.IEEE Trans.Automatic Control,1995,40:983-993
8． Lin W.Global asymptotic Stabilization of general Nonlinear Systems with stable Free Dynamics via passivity and bounded feedback.Automatica,1996,32(6) :915-924
9． Ortega R.Passivity properties for stabiliztion of cascaded nonlinear systems.Automatica,1991,27(2) :423-424
10． Lin W,Shen T.Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty.Automatica,1999,35:35-47
11． 申铁龙．机器人鲁棒控制基础．北京：清华大学出版社，2000：66-77
12． Mei Shenwei,Shen T.Sun Y,Lu Q.Passivation control of nonlinear systems with disturbances.Control Theory and Applications,1999,16(6) :797-801
13． Teel A R,Praly L.On assigning the derivative of disturbance attenuation control Lyapunov function.MCSS,2000,3:95-124
14． Jiang Z P,Hill D J.Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems.IEEE Trans.Automat.Contr.,1998,43(7) :992-997
15． Isidori A,Astolfi A.Disturbance attenuation and H-infinite control via measurement feed-back in nonlinear systems.IEEE Trans.Automatic Control,1992(37) :1283-1293
16． A J van der Schaft.L2-gain and passivity techniques in nonlinear control.2nd ed.Lecture Notes in Control and Information Sciences.vol 218． Springer:Berlin,1996
17． Sontag E D.Smooth stabilization implies coprime factorization.IEEE Trans.Automa.Contr.,1989,34(4) :435-443
18． Sontag E D,Wang Y.On characterizations of the input-to-state stability property.Syst.Contr.Lett.,1995,24:351-359
19． Jiang Z P,Teel A R,Praly L.Small-gain theorem for ISS systems and applications.MCSS,1994(7) :95-120
20． Krstic M,Li Z.Inverse optimal design of input-to-state stabilizing nonlinear controllers.IEEE Trans.Automatic Control,1998,43:336-349
21． Jiang Z P,Mareels I M and Wang Y.A Liapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems.Automatica,1996,32(8) :1211-1215
22． Arack M.Seron M,Bravsky J,Kokotovic P.Robustification of backstepping against input unmodeled dynamics.IEEE Trans.Automa.Contr.,2000,45(8) :1-6
23． Sontag E D.A universal construction of Artstein's theorem on nonlinear stabilization.Syst.Contr.Lett.,1989,13:117-123
24． Moylan P J.Implications of passivity in a class of nonlinear systems.IEEE Trans.Automa.Contr,1974,18:373-381．
25． Pomet J B.Explicit design of time varying stabilizing control laws for a class of controllable systems without drift.Syst.Contr.Lett.,1992,18:147-158
26． Bensoubaya M,Ferfera A,Iggidr A.A Jurdjevic-Quinn type theorem for nonlinear systems.In Proc.37th IEEE CDC,December,1998:2485-2490
27． Mazenc F,Praly L.Adding integrators,saturated controls and stabilization for feedforward systems.IEEE Trans.Autom.Contr.,1996,41(11) :1559-1578
28． Brogliato B,Laudau I,Lozano R.Adaptive motion control of robot manipulators:a unified approah based on passivity.Int J Robust and Nonlinear control,1991,1:187-202
29． Lu Weiming,Packard A.Adaptive H-infinite control for nonlinear systems:a dissipation theor-etical approach.Caltech CDS Tech.Memo.,No.CIT-CDS-96-019,1996．
30． Luenberger D G.Optimization by vector space metods.New Ydrk:John Wiley & Sons,Inc.,1969
31． Marino R,Tomei P.Observer-based adaptive stabilization for a class of nonlinear systems. Automatica,1992,28:787-793
32． Sontag E D.Further facts on input to state stabilization.IEEE Trans.Automa.Contr.,1990,35(4) :437-442
33． Sontag E D.Teel A.Changing supply functions in input/state stable systems,IEEE Trans.Autom.Contr.,1995,40:1476-1478
34． Sontag E D.Wang Y.A notion of input-to-output stability.In Proc.European Control Conf.,Brussel,July,1997
35． Angeli D.Input-to-state stability of PD-controlled robotic systems.Automatica,1999,35:1285-1290
36． Liu W.Chitour Y,Sontag E D.On finite-gain stabilizability of linear systems subject to input saturation.SIAM J Control and Optimization,1996,34(4) :1190-1219
37． Teel A R.A nonlinear small gain theorem for the analysis of control systems with saturation.IEEE Trans.Automa.Contr.,1996,41(9) :1256-1270
38． Byrnes C I,Isidori A.New results and examples in nonlinear feedback stabilization.Syst.Contr.Lett.,1989,12:437-442．
39． Sussmann H J,Sontag E D,Yang Y.A General Result on the Stabilization of Linear Systems Using Bounded Controls.EEEE Trans.Automat.Contr.,1994,39:2411-2425
40． Artstein Z.Stabilization with relaxed controls.Nonlinear analysis,1983,7:1163-1173
41． Clarke F H,Ledyaeve Y S,Sontag E D,Subbotin A I.Asymptotic controllability implies feedback stabilization.IEEE Trans.Autom.Contr.,1997,42:1394-1407
42． Bacciotti A.Local stabilizability of nonlinear control systems.Series on advances in mathema-tics for applied sciences,World Scientific,1992
43． 高为炳．变结构控制理论基础．北京：中国科学出版社，1990
44． Qin Huashu,Hong Yiguang.Passivity.stability and optimality.Control Theory and Applica-tions,1994,11 (4) :421-427
45． Shiriaev A S.The Notion of V-detectability and Stabilization of Invariant Sets of Nonlinear Systems.Proceedings of the 37 IEEE Conference on Decision & Control,Tempa,Florida,USA,1998
46． Glad S T.Robustness of Nonlinear State Feedback-A Survey.Automatica,1987,23:425-435
47． Krstic M.Kanellakopoulos I,Kokotovic P.Nonlinear and adaptive control design.New York:Wiley,1995
48． Sontag E D.Mathematical control theory-deterministic finite dimensional syste-ms.New York:Springer-Verlag,1990
49． Vidyasagar M.Decomposition techniquues for large-scare systems with non-additive interac-tions:stability and stabilizability.IEEE Trans.Automat.Control,1980(25) :773-779
50． Andriano V,Bacciotti A,Beccari G.Global stability and external stability of dynamic systems.Nonlinear Analysis,1997(28) :1167-1185
51． Iggidr A.kalitine B.Outbib R.Semi-definite Lyapunov functions.stability and stabilization.MCSS,1996,9:95-106
52． Carr J.Applications of center manifold theory.New York:Springer-Verlag,1981
53． Faubourg L.Pomet J B.Strict control Lyapunov functions for homogeneous Jurdjevic-Quinn type systems.In Nonlinear Control Systems Design Symphosium,IFAC,1998:823-829
54． Morin P.Robust stabilization of the angular velocity of a rigid body with two actuators.European J of Control,1996,2(1) :51-56
55． Doyle J C.Glover K,Khagonekar P.Francis B A.State-space solution to standard H2 and H-infinite control problem.IEEE Trans.Automatic Control,1989,34:831-842
56． Ball J A,Kachroo P,Krener J A.H-infinite tracking control for a class of nonlinear systems.IEEE Trans.Autom.Contr.,1999,44(6) :1202-1206
57． Isidori A,Byrnes C I.Optimal regulation of nonlinear systems.IEEE Trans.Autom.Contr.1990,35(2) :131-140