摘要
时滞现象由于其深刻的实际背景已经引起广泛的关注.时滞通常是系统不稳定和性能恶化的主要根源之一.利用现有的时滞系统稳定性分析方法得到的往往是充分条件,降低结果的保守性是控制算法实用化、工业化的关键环节,目前还缺乏有关稳定性准则保守性的系统论述.
针对标称线性时滞系统,本论文提出稳定性准则的等价性定义,深入研究稳定性准则的保守性问题.基于Lyapunov-Krasovskii稳定性理论,采用线性矩阵不等式工具,对奇异时滞系统、Lur'e时滞系统、Markov跳变时滞系统以及时滞细胞神经网络系统进行稳定性分析,并结合系统各项性能指标给出控制器的设计方法.进而以网络控制系统为应用背景,深入研究网络控制系统特有的问题,如:时滞、丢包和量化等对系统性能的影响,设计控制器使得网络闭环系统渐近稳定.最后,以蒸馏塔为研究对象,将本论文提出的状态反馈迭代控制方法应用于蒸馏塔控制系统仿真.论文的主要工作如下:
(1)针对现有的线性时滞系统稳定性分析方法,从理论上证明了其中某些方法的等价性,改变了目前以数值例子来验证结果有效性的处理方法,进而给出判断自由变量是否是冗余变量的有效手段,得出自由变量法更适于多胞型不确定时滞系统的结论.
(2)应用积分不等式处理方法,分别导出了奇异时滞系统、Lur'e时滞系统、Markov跳变时滞系统以及时滞细胞神经网络系统的时滞相关稳定性条件,并提出了基于线性矩阵不等式求解的状态反馈稳定化控制器设计方法.从理论上证明了所导出的结果具有更小的保守性.其中奇异时滞系统的稳定性条件同时保证了系统正则、无脉冲.进一步,结合系统的二次性能指标,给出了奇异时滞系统和Lur'e时滞系统保性能控制器的设计方法,结合系统的增益性能和相位性能指标,给出Markov跳变时滞系统耗散性控制器的设计方法.
(3)应用积分不等式处理方法,导出具有时变时滞的网络控制系统稳定性条件,该条件克服了传统方法对时滞变化上界的依赖,允许时滞是快变的,更符合网络控制的实际情况.进一步研究丢包对状态估计的影响以及丢包的补偿策略,并结合系统的扰动抑制性能指标,给出使得时滞最大化的H_∞控制器设计方法.最后,给出保证闭环网络控制系统稳定的量化反馈控制器的设计方法,并揭示了数据丢包率、时滞和平均数率之间的量化关系.
(4)应用本论文给出的算法对蒸馏塔控制系统进行仿真,仿真结果验证了该方法的可行性和良好的性能.这一部分内容是时滞系统理论面向实际工程问题的尝试性应用.
Time-delay phenomenon has received much attention due to its profound practical background and time-delays are often the source of instability and degradation in control performance. By using the existing stability analysis methods, sufficient conditions are often obtained and reducing the conservatism is important for the practicality and industrialization of the control algorithm. However, there are few systematical discussions about the conservatism of the stability criteria.
For nominal linear time-delay systems, the equivalence of stability criteria is defined and the conservatism of the stability criteria is deeply analyzed. Based on Lyapunov-Krasovskii stability theory, the stability analysis of singular time-delay systems、Lur'e time-delay systems、time-delay systems with Markovian parameters、delayed cellular neural networks systems are proposed in this dissertation and the sufficient conditions for the existence of the controller are derived with respect to the performance. Some characteristics of network control systems are deeply studied, such as: time-delay, packet-drop out, quantization and the state feedback controller is designed which guarantees the closed-loop system stable. Finally, state feedback control algorithm developed in this dissertation is applied in the process of a distillation column control system simulation. The main contents of this dissertation are outlined as follows:
(1) For linear time-delay systems, some stability analysis methods are proved theoretically to be equivalent, which is different from the regular practice that most of the criteria are compared via numerical examples. Furthermore, a method is given to judge if a slack variable is redundant. Finally, we concluded that the slack variable method is more suitable to deal with polytopic uncertain systems.
(2) For singular time-delay systems、Lur'e time-delay systems、time-delay systems with Markovian parameters and delayed cellular neural networks systems, the integral inequality method is used to derive the delay-dependent stability criteria, based on which the controller design problem are formulated as the solvability of some iterative linear matrix inequalities. It is proved theoretically that the results obtained in this dissertation are less conservative than some existing results. The stability criteria obtained for singular time-delay systems also guarantee the system regular and impulse free. The controller is designed which satisfied the proposed guaranteed cost and dissipative performance.
(3) For the networked control systems with time-varying time-delay, the integral inequality method is used to derive the stability criteria. The criteria are independent of the delay derivative bound, e.g., the delay considered here is allowed to be fast-varying, which is more suitable for networked control systems. Furthermore, the analysis is focused on how the packet dropping affects state estimation and what we can do to compensate this unreliability. The H_∞controller is obtained which allows a maximum allowable delay size for a fixed disturbance rejection performance value. Finally, the quantized feedback controller is designed which guarantees the Lyapunov stability of closed-loop systems. Besides, the relationship among the packet-dropping rate, time delay and the average data rate is also obtained in the meanwhile.
(4) The state feedback control strategy developed in this dissertation is applied for the distillation column control system simulation. Simulation results demonstrate the validity and excellent performance of this method. This part constitutes an attempt of applying the Lyapunov stability idea to practical engineering problems.
引文
[1]Niculescu S I.Delay Effects on Stability[M].London,Springer-Verlag,2001.
[2]Stepan G.Retarded Dynamical Systems:Stability and Characteristic Functions[M].Essex:Longman Scientific and Technical,1989.
[3]Kuang Y.Delay Differential Equations with Applications to Population Dynamics[M].New York:Academic Press,1993.
[4]Bellman R,Cooke K.Differential Difference Equations[M].New York,Academic Press,1963.
[5]Kolmanovskii V B,Myshkis A.Introduction to the Theory and Application of Functional Differential Equations[M].Dordrecht:Kluwer Academy,1999.
[6]Hale J K.Theory of Function Differential Equations[M].New York:Spinger-Verlag,1977.
[7]秦元勋,刘永清,王联.带有时滞的动力系统的稳定性[M].第二版.北京:科学出版社,1989.
[8]胡海岩,王在华.非线性时滞动力系统的研究进展[J].力学进展,1999,29(4):501-512.
[9]Just W,et al.Mechanism of time-delayed feedback control[J].Phys Rev Lett,1997,78(2):203-206.
[10]Nikiforuk P,Westlund,D.Relative stability from the dual-locus diagram[J].IEEE Trans.Automat.Contr,1965,10(1):103-104.
[11]Mukherjee S K.Note on the stability of linear control system with distributed-lag[J].Journal of the Institution of Electronics and Telecommunication Engineers,1975,21(2):75-76.
[12]Zhong Q C.Robust stability analysis of simple systems controlled over communication networks[J].Automatica,2003,39(7):1309-1312.
[13]Zhong Q C.Control of integral processes with dead time-Part 3:Deadbeat disturbance response[J].IEEE Trans.Automat.Contr,2003,48(1):153-159.
[14]Olgac N,Holm-Hansen,B.Design considerations for delayed-resonator vibration absorbers[J].Journal of Engineering Mechanics,1995,121(1):80-89.
[15]Chiasson J N.A method for computing the interval of delay values for which a differential-delay system is stable[J].IEEE Trans.Automat.Contr,1988,33(12):1176-1178.
[16]Thowsen A.The Routh-Hurwitz method for stability determination of linear differential-difference systems[J].Int.J.Control,1981,33(5):991-995.
[17]Watanabe,K,Nobuyama,E,Kitamori,T et al.A new algorithm for finite spectrum assignment of single-input systems with time delay[J].IEEE Trans.Automat.Contr,1992,37(9):1377-1383.
[18]Suyama K.Finite spectrum assignment for linear systems with non-commensurate time-delays[J].Automatica,2001,37(1):43-49.
[19]Pontryagain L S.On the zeros of some elementary transcendental functions[J].American Mathematic Socierty,1955,2(1):95-110.
[20]Rekasius Z V.A stability test for systems with delays[A].Proc of the Joint Automatic Control Conference, San Francisco,CA,August,1980,Paper No.TP9-A.
[21]Olgac N,Sipabi,R.An exact method for the stability analysis of time-delayed linear time-invariant(LTI)systems[J].IEEE Trans.Automat.Contr,2002,47(5):793-797.
[22]Walton K,Marshall J E.Direct method for TDS stability analysis[J].IEE Proc.,Part D:Control Theory and Applications,1987,134(2):101-107.
[23]Zhang J,Knopse C R,Tsiotras P.Stability of time-delay systems:Equivalence between Lyapunov and scaled small-gain conditions[J].IEEE Trans.Automat.Contr,2001,46(3):482-486.
[24]Xu B G.Stability criteria for linear time-invariant systems with multiple delays[J].Journal of Mathematical Analysis and Applications,2000,252(1):484-494.
[25]俞元洪.超越函数det(a_(ij)+b_(ij)e~(-λτ)-δ_(ij)λ)零点全分布在复平面左半部的代数判定[J].科学通报,1984,29(23):1413-1415.
[26]刘和涛.一类时滞微分系统无条件稳定的代数判定[J].控制理论与应用,1986,3:106-110.
[27]张作元.滞后型方程(?)(t)=Ax(t)+Bx(t-τ)全时滞稳定的代数判据[J].数学通报,1986,31(23):1768-1771.
[28]Repin Y M.Quadratic Lyapunov functionals for systems with delay[J].[Russian]Prikladnaya Matematika Mehanika,1965,24(3):564-566.
[29]Brierley S D,Lee E B.Solution of the equation A(z)X(z)+X(z)B(z)= C(z)and its application to the stability of generalized linear systems[J].Int.J.Control,1984,40(6):1065-1075.
[30]Lee E B,Lu W S,Wu N E.A Lyapunov theory for linear time-delay systems.IEEE Trans.on Auto.Contr.1986,31:259-261.
[31]Agathoklis P,Foda S.Stability and the matrix Lyapunov equation for delay differential systems.Int.J.Control,1989,49(2):417-42.
[32]廖小昕.动力系统的稳定性理论和应用[M].北京:国防工业出版社,2000.
[33]Lefschitz.Stabilty of Nonlinear Control Systems[M].New York:Academic Press,1965.
[34]Razumikin B S.On the stability of systems with delay[J].Prikladnava Matematikal Mekhanika,1956,20(4):500-512.
[35]Trinh H,Aldeen M.On robustness and stabilization of linear systems with delayed nonlinear perturbations[J].IEEE Trans.Automat.Contr,1997,42(7):1005-1007.
[36]Park P.Delay-dependent stability criteria for systems with uncertain time-varying delays[A].Proc of American Control Conference,San Diego,U.S.A.1998,1963-1965.
[37]Jankovic M.Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems[J].IEEE Trans.Automat.Contr,2001,46(7):1048-1060.
[38]Liu Y Q.On the equivalence problem of control systems and control systems with time-lags in the theory of stabilization(1),(2)[A].Proc of 9th World Congress of IFSC,105,Budapest,Hungary,1984,2-6.
[39]Gu K,Kharitonov V L,Chen J.Stability of Time-delay Systems[M].Boston:Birkhauser,2003.
[40]Han Q L,Jiang X F,M X.Computation of delay bound for linear neutral systems with interval time-varying discrete delay[J].Dynamics of Continuous,Discrete and Impulsive Systems,Series B:Applications & Algorithm,2006,13(c):117-131.
[41]Krasovskii N N.Stability of Motion[M].Stanford University Press,Stanford CA,USA,1963.(translation by J.Brenner).
[42]Boyd S,El Ghaoui L,Feron E,Balakrishnan V.Linear Matrix Inequalities in System and Control Theory[M].Philadelphia,PA:SIAM,1994.
[43]俞立.鲁棒控制一线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.
[44]俞立.一类时滞系统的绝对稳定性问题研究[J].自动化学报,2003,29(3):428-431.
[45]段广仁,刘湘黔.线性时滞系统时滞独立稳定的充分条件[J].控制与决策,1996,11(3):420-423.
[46]Gu K Q.Discretized Lyapunov functional for uncertain systems with multiple time delay[J].Int.J.Control,1997,72(16):1436-1445.
[47]Gu K Q,Niculescu S I.Additional dynamics in transformed time-delay systems[J].IEEE Trans.Automat.Contr,2000,45(3):572-575.
[48]Park R A delay-dependent stability criterion for systems with uncertain time-invariant delays[J].IEEE Trans.Automat.Contr,1999,44(4):876-877.
[49]Moon Y S,Park P,Kwon W H,Lee Y S.Delay-dependent robust stabilization of uncertain state-delays systems[J].Int.J.Control,2001,74(14):1447-1455.
[50]Fridman E,Shaked U.A descriptor system approach to H∞ control of linear time-delay systems[J].IEEE Trans.Automat.Contr,2002,47(2):253-270.
[51]Fridman E,Shaked U.Delay-dependent stability and H∞ control:constant and time-varying delays[J].Int.J.Control,2003,76(1):48-60.
[52]Fridman E,Shaked U.An improved stabilization method for linear time-delay systems[J].IEEE Trans.Automat.Contr,2002,47(11):1931-1937.
[53]Han Q L.Absolute stability of time-delay systems with sector-bounded nonlinearity[J].Automatica,2005,41(12):2171-2176.
[54]Zhang X M,Wu M,She J H,He Y.Delay-dependent stabilization of linear systems with time-varying state and input delays[J].Automatica,2005,41(8),1405-1412.
[55]He Y,Wu M,She J H,Liu G R Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type Uncertainties[J].IEEE Trans.Automat.Contr,2004,49(5):828-832.
[56]Rosenbrock H H.Structural properties of linear dynamical systems[J].Int J.Contr,1974,20(2):191-202.
[57]Luenberger D G,Arbel A.Singular dynamical Leontif systems[J].Econometrica,1977,45(4):991-995.
[58]徐胜元.广义不确定系统的鲁棒控制[D].南京理工大学博士论文,2002.
[59]Rosenbrock H H,Pugh A C.Contributions to a hierarchical theory of systems[J].Int.J.Contr,1974,19:845-867.
[60]Campbell S L,Nichols N K,Terrel,W J.Duality,observability,and controllability for linear time-varying descriptor systems[J].Circ.Syst.Sig.Process,1991,10(4):455-470.
[61]Karcanias N.Proper invariant realizations of singular system problems[J].IEEE Trans.Automat.Contr,1990,35(2):230-233.
[62]Gaddouna B,Giuliani S,Ragot J.Design of observers for descriptor systems affected by unknown inputs[J].Int.J.Syst.Sci,1996,27(5):465-471.
[63]Fletcher L R,Aasaraai A.On disturbance decoupling in descriptor systems[J].SIAM J.Control Optim,1989,27(6):1317-1332.
[64]Fletcher L R.Pole assignment and controllability subspaces in descriptor systems[J].Int.J.Contr,1997,66(5):677-709.
[65]Shayman M A.Pole placement by dynamic compensation for descriptor systems[J].Automatica,1987,24(2):279-282.
[66]De L S M.On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays[J].Applied Mathematics and Computation,2007,190(1):382-401.
[67]Fang C,Chang F.Analysis of stability robustness for generalized state-space systems with structured perturbations[J].Syst Contr.Lett,1993,21(2):109-114.
[68]Krasovskii N N,Lidskii E A.Analytical design of controllers in system with random attributes Ⅰ,Ⅱ,Ⅲ,Automation Remote Contr,1961,22:1021-1025,1141-1146,1289-1294.
[69]Cao Y Y,Lain J.Robust control of uncertain Markovian jump systems with time-delay[J].IEEE Trans.Automat.Contr,2000,45(1):77 - 83.
[70]Chen W H.Guaranteed control for uncertain Markovian jump systems with mode-dependent time-delays[J].IEEE Trans.Automat.Contr,2003,48(1):2270-2276.
[71]Cao Y Y.Delay-dependent stochastic stability and analysis for time-delay systems with Markovian jumping parameters[J].J Franklin Inst,2003,340(1):423-434.
[72]Boukas E K.Robust control of discrete-time Markovian jump linear systems with mode-dependent time-delays[J].IEEE Trans.Automat.Contr,2001,46(1):1918-1924.
[73]Mao X.Stability of stochastic differential equations with Markovian switching[J].Stochastic Process.Appl.1999,79(1):45-67.
[74]Feng X,Loparo K A,Ji Y,Chizek H J.Stochastic stability properties of jump linear systems[J].IEEE Trans.Automat.Contr,1992,37(1):38-53.
[75]Ji Y,Feng,H.Chizeck J.Controllability,stabilizability,and continuous-time Markov jump linear quadriatic control[J].IEEE Trans.Automat.Contr,1990,35(1):777-788.
[76]Benjillon K,Boukas E K.Independent delay sufficient conditions for robust stability of uncertain linear time-delay systems with jumps[C].Proc of American Control Conference,Albuquerque,NM,1997,3814-3815.
[77]Wang Z,Qiao H,Burnham K J.On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters[J].IEEE Trans Automat Contr,2002,47(4):640-646.
[78]Mao X,Matasov A,Piunovskii A B.Stochastic differential delay equations with Markovian swicthing[J].Bernoulli,2000,6:73 -90.
[79]Wang Y,Xie L,De Souza C E.Robust control of a class of uncertain nonlinear systems[J].Syst Contr Lett,1992,19(2):139-144.
[80]Mahmoud M S,Al-Muthairi N F.Design of robust controllers for time-delay systems[J].IEEE Trans.Automat.Contr,1994,39(5):995-999.
[81]Li Z H,Wang J C,Shao H H.Delay-dependent dissipative control for linear time-delay systems[J].J Franklin Inst,2002,339(1):529-542.
[82]Willem J C.Dissipative dynamical systems-Part Ⅰ:general Theory[J].Archive for Mechanics Analysis,1972,45(5):321-351.
[83]Willem J C.Dissipative dynamical systems-Part Ⅱ:linear systems with quadratic supply rates[J].Archive for Rational Mechanics Analysis,1972,45(5):352-393.
[84]Hill D J.Moylan P J.Dissipative dynamical systems:basic input-output and state properties[J].J Franklin Inst,1980,309(5):327-357.
[85]关新平,华长春,段广仁.不确定时滞系统的鲁棒耗散性研究[J].系统工程与电子技术,2002,24(1):48-51.
[86]Lozano R,Brogliato B Z,Egeland O,et al.Dissipative Systems Analysis and Control[M].London:Kluwer Academic Publishers,2000.
[87]兰海.基于耗散理论的电力系统鲁棒非线性控制研究[D].哈尔滨,哈尔滨工程大学博士论文,2004.
[88]邵汉永,冯纯伯.二次型耗散线性离散系统的鲁棒性分析与控制[J].控制与决策,2005,20(2):142-146.
[89]关新平,华长春,龙承年。不确定非线性系统的鲁棒耗散性与保性能控制[J].控制理论与应用,2003,20(6):938-942.
[90]Trentelman H L,Willems J C.Every storage function is a state function[J].Systems & Control Letters,1997,32(5):249-259.
[91]Belur M N,Trentelman H L.The strict dissipativity synthesis problem and the rank of the coupling QDF[J].Systems & Control Letters,2004,51(3-4):247-258.
[92]冯纯伯.应用无源性分析研究时变非线性系统的稳定性[J].自动化学报,1997,23(6):775-781.
[93]Anderson B D O.The small-gain theorem,the passivity theorem,and their equivalence[J].J Franklin Inst,1972,293(2):105-115.
[94]Xie S L,Xie L H.Robust dissipative control for linear systems with dissipative uncertainty and nonlinear perturbation[J].Systems & Control Letters,1997,29(5):255- 268.
[95]刘飞,苏宏业,褚健.线性离散时滞系统鲁棒严格耗散控制[J].自动化学报,2002,28(6):897-903.
[96]Gan Z X,Han J Q.Lyapunov function of general Lurie systems with multiple nonlinearities[J].Appl.Math.Lett,2003,16:119-126.
[97]Grujic L T.On absolute stability and Aizerman conjecture[J].Automatica,1981,17:335-349.
[98]Narendra K S,Taylor J H.Frequency Domain Criteria for Absolute Stability[M].Academic Press,New York,1973.
[99]Popov V M.Absolute stability of nonlinear systems with delay[J].Automat.Remote Control,1962,22(7):849-851.
[100]Zhao S X.On absolute stability of control systems with several executive elements[J].Sci.Sinica Ser.A,1988,31:395-405.
[101]Grujic L J T,Petkovski D J.On robustness of Lurie system with multiple non-linearities[J].Automatica,1987,23(2):327-334.
[102]Tesi A,Vicino A.Robust absolute stability of lur'e control systems in parameter space[J].Automatica,1991,27(1):147-151.
[103]年晓红.Lurie型控制系统的鲁棒绝对稳定性[J].控制理论与应用,1995,12(5):641-645.
[104]杨斌,潘德惠.关于Lurie型控制系统的鲁棒绝对稳定性[J].自动化学报,1998,24(6):816-819.
[105]Popv V M,Halanay A.About stability of nonlinear controlled systems with delay[J].Automat Remote Control,1962,23(7):849-851.
[106]Kolmanonovskii V B,Nosov V R.Stability of Functional Differential Equations[M].New York:Academic Press,1986.
[107]Somolines A.Stability of Lurie-type functional equations[J].J Diff Eqs,1977,26(2):191-199.
[108]年晓红.Lur'e控制系统绝对稳定的时滞相关条件[J].自动化学报,1999,25(4):564-566.
[109]年晓红,黄力民.Lur'e滞后反馈控制系统绝对稳定的鲁棒扰动界[J].信息与控制,2001,30(2):155-158.
[110]Gan Z X,Ge W G..Lyapunov functional for multiple delay general Lur'e control systems with multiple non-linearities[J].J.Math.Anal.Appl,2001,259:596-608.
[111]He Y,Wu M.Absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities[J].J.Comput.Appl.Math,2003,159:241-248.
[112]He Y,Wu M,She J H,Liu G P.Robust stability for delay Lur'e control systems with multiple nonlinearities[J].J.Comput.Appl.Math,2005,176(2):371-380.
[113]Han Q-L.Absolute stability of time-delay systems with sector-bounded nonlinearity[J].Automatica,2005,41(12):2171-2176.
[114]Zhang X M,Wu M,She J H et al.Delay-dependent stabilization of linear systems with time-varying state and input delays[J].Automatica,2005,41(8):1405-1412.
[115]Chua L O,Yang L.Cellular neural networks:Theory[J].IEEE Trans.Circuits Syst.,1998,35(10):1257-1272.
[116]Chua L O,Roska T.Celular neural networks with nonlinear and delay-type template element[C].Proc of CNNA,1990,90:12-25.
[117]Forti M.On global asymptotic stability of a class of nonlinear systems arising in neural network theory.J DiffEqs,1994,113:246-264.
[118]Forti M,Tesi A.New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Trans.on circuits and systems-I:Fundament theory and applications,1995,42(7):354-366.
[119]Chua L O,Yang L.Cellular neural networks:Applications[J].IEEE Trans.Circuits Syst.Ⅰ,1988,35(10):1273-1290.
[120]Roska T,Chua L O.Cellular neural networks with non-linear and delay-type template elements and non-uniform grids[J].Int.J.Circuit Theory Appl,1992,20:469-481.
[121]焦李成.神经网络的应用和实现[M].西安:西安电子科技大学出版社,1996.
[122]Roska T,Wu C W,Balsi M,Chua L O.Stability and dynamics of delay-type general and cellular neural networks[J].IEEE Trans.Circuit and Systems-I,1992,39(6):487-490.
[123]Zhang Y,Zhong S M,Li Z L.Periodic solutions and stability of Hopfield neural networks with variable delays[J].Int J Syst Sci,1996,27:895-901.
[124]Zhang Q,Wei X,Xu J.Global exponential convergence analysis of delayed neural networks with time-varying delays[J].Phys Lett A,2003,318(6):537-544.
[125]Philips S M,Tilbury D M,Moyne J R,Fridman E.Discussion on:"Stabilization of networked control systems with data packet dropout and transmission delays:continuous-time case".European Journal of Control,2005,11(1):50-55.
[126]Luck R,Ray A.An observer-based compensator for distributed delays[J].Automatica,1990,26(5):903-908.
[127]樊卫华,蔡骅,陈庆伟,胡伟礼.时延网络控制系统的稳定性[J].控制理论与应用,2004,21(6):880-884.
[128]Lin H,Antsaklis P J.Stability and persistent disturbance attenuation properties for a class of networked control systems:switched system approach[J].Int J.Contr,2005,78(18):1447-1458.
[129]Yu M,Wang L,Chu T.Sampled-data stabilization of networked control systems with nonlinearity[J].IEE Proceedings Control Theory & Applications,2005,152(6):609-614.
[130]Zhang W.Stability analysis of Networked control systems[D].PhD thesis,Case Western Reserve University,2001.
[131]Ling Q,Lemmon Michael D.Robust performance of soft real-time networked control systems with data dropouts[C].Proc of IEEE Conference of Decision and Control,Las Vegas,Nevada USA,2002,1225-1230.
[132]Ling Q,Lemmon Michael D.Soft real-time scheduling of networked control systems with dropouts governed by Markov chain[C].Proc of IEEE American Control Conference,Denver,Colorado,2003,4845- 4850.
[133]Yue D,Han Q.L,Peng C.State feedback controller design of networked control systems[J].IEEE Trans.on circuits and systems -Ⅱ,2004,51(11):640-644.
[134]Ling S,Richard M.M.Towards a packet-based control theory - part ii:rate issues[C].Proc of IEEE American Control Conference,Minneapolis,2006,3482- 3487.
[135]Hassibi A,Boyd S P,How J P.Control of asynchronous dynamical systems with rate constraints on events[C].Proc of IEEE Conf.Decision and Control,Phoenix,1999,2(1):345-351.
[136]Hu S,Yah W Y.Stability robustness of networked control systems with respect to packet loss[J].Automatica,2007,43(7):1243-1248.
[137]Yu M,Wang L,Xie G M,Chu T G.Stabilization of networked control systems with data packet dropout via switched system approach[C].IEEE International Symposium on Computer Aided Control Systems Design,Taiwan,2004,362-367.
[138]Seller P,Sengupta R.An H∞ approach to networked control[J].IEEE Trans.Automat.Contr,2005,50:356-364.
[139]Xiong J L,Lam J.Stabilization of linear systems over networks with bounded packet loss[J].Automatica,2007,43(1):80-87.
[140]Girish N,N,Fagnani S Z,Robin J E.Feedback control under data rate constraints:an verview[C].Proc of the IEEE,2007,95(1):108-37.
[141]Tatikonda S,Sahai A,Mitter S.Control of LQG systems under communication constraints[C].Proc of the IEEE Conference on Decision and Control,1998,1165-1170.
[142]Fu M Y,Xie L H.The sector bound approach to quantized feedback control.IEEE Trans.Automat.Contr,2007,50(11):1698-1711.
[143]Ling S,Richard M M.Toward a packet-based control theory- Part I:stabilization over a packet-based network[C].Proc of 2005 American Control Conference.http://www.cds.caltech.edu/-murray/papers/2004z_sm05b-acc.html.
[144]白涛,吴智铭,杨根科.网络化控制系统带宽配置的一种新策略[J].自动化学报,2004,30(6),961-967.
[145]李金库,高磊,王磊,张德运.一种基于网络处理器的动态带宽分配算法[J].西安交通大学学报.2005,39(12):1323-1326.
[146]Yook J K,Tilbury D M,Soparkar N R.Trading computation for bandwidth:reducing communication in distributed control systems using state estimators[J],IEEE Trans.on Control Systems Technology,2002,10(4):503-518.
[147]Ishii,H,Francis B A.Stabilizing a linear system by switching control with dwell time[J],IEEE Trans.Automat.Contr,2002,47(12):1962-1973.
[148]朱其新.网络控制系统的建模、分析与控制[D].南京航空航天大学博士论文,2003.
[149]樊卫华.网络控制系统的建模与控制[D].南京理工大学博士论文,2004.
[150] Xu S Y, Lam J. Improved delay-dependent stability criteria for time-delay systems[J]. IEEE Trans. Automat. Contr, 2005, 50(3): 384-387.
[151] Lee Y S, Moon Y S, Kwon W H, Park P G. Delay dependent robust H_∞ control for uncertain systems with a state-delay[J]. Automatica, 2004,40(1): 65-72.
[152] Jing X J, Tan D L, Wang Y C. An LMI approach to stability of systems with severe time-delay [J]. IEEE Trans. Automat. Contr, 2004: 49(7): 1192-1195.
[153] Kolmanovskii V B, Niculescu S I, Richard J P. On the Lyapunov-Krasovskii function for stability analysis of linear delay systems[J]. Int. J. Control, 1999b, 72(4): 374-384.
[154] Infante E F, Castelan W B. A Lyapunov functional for a matrix difference-differential equation[J]. J Diff Eqs, 1978,29,439-451.
[155] Gu K Q. A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems[J]. International Journal on Robust and Nonlinear control, 1999a, 9(1): 1-14.
[156] Gouaisbaut F, Peaucelle D. Delay-dependent robust stability of time delay systems[C]. Proc of 5th IFAC Symposium on Robust Control Design, Toulouse, France, 5-7, 2006.
[157] Haddad W M, Bernstein D S. Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis[J]. IEEE Trans. Automat. Contr, 1995,40(3): 536-543.
[158] Gahinet P, Apkarian P, Chilali M. Affine parameter-dependent Lyapunov functions and real parametric uncertainty [J]. IEEE Trans. Automat. Contr, 1996, 41(3): 436-442.
[159] Feron E, Apkarian P, Gahinet P. Analysis and synthesis of robust control systems via parameter- dependent lyapunov functions[J]. IEEE Trans. Automat. Contr, 1996, 41(7): 1041-1046.
[160] Oliveira M C, Bernussou J, Geromel J C. A new discrete-time robust stability condition[J]. Systems & Control Letters, 1999, 37(4): 261-265.
[161] Lin C, Wang Q G, Lee TH. A less conservative robust stability test for linear uncertain time-delay systems[J]. IEEE Trans. Automat. Contr, 2006, 51(1): 87-91.
[162] Papachristodoulou A, Peet M, Lall S. Constructing Lyapunov-Krasovskii functionals for linear time delay systems[C]. Proc of American Control Conference, 2005,4: 2845-2850.
[163] Parrilo P A. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization[D]. PhD Dissertation, California Institute of Technology, USA, 2000.
[164] Lasserre J B. Global optimization with polynomials and the problem of moments[J]. SIAM Journal on Optimization, 2001, 11(3): 796-817.
[165] Henrion D, Garulli A. Positive Polynomials in Control[M]. Berlin Heidelberg, Springer-Verlag, 2005.
[166] Suplin V, Fridman E, Shaked U. A projection approach to H_∞ control of time-delay systems[C]. Proc of 43th Decision and Control Conference, Atlantis, Bahamas, 2004, 4548- 4553.
[167] Gouaisbaut F, Peaucelle D. A note on stability of time delay systems[C]. Proc of ROCOND, Toulouse, France, 2006, 5-7.
[168] Peaucelle D, Gouaibaut F. "Discussion on 'parameter-dependent Lyapunov functions approach to stability analysis and design for uncertain systems with time-varying delay'"[J]. European Journal of Control, 11(1): 69-70,2005.
[169] Gouaisbaut F, Peaucelle D. Stability of time-delay systems with non-small delay[C]. Proc of 45th Decision and Control Conference, San-Diego, USA, 2006, 840-845.
[170] Wang S S, Chen B S, Lin T P. Robust stability of linear systems with a single time delay[J]. Int. J. Contr. 1987, 46(3): 963-976.
[171] Su J H. Further results on the robust stability of linear systems with a single time delay[J]. System & Control Letters, 1994, 23(6): 375-379.
[172] Lee J H, Kim S W, Kwon W H. Memoryless controllers for state delayed systems[J]. IEEE Trans. Automat. Contr, 1994, 39(1): 159-162.
[173] Li X, De Souza C E. Criteria for robust stability of uncertain linear systems with time-varying state delays[C]. Proc of 13th IFAC World Congr, 1996,1, 137-142.
[174] Niculescu S I, Neto A T, Dion J M, Dugard L. Delay-dependent stability of linear systems with delayed state: An LMI approach[C]. Proc. of 34th Decision and control conference, 1995, 2, 1495-1496.
[175] Niculescu S I, De souza C E, Dion J M, Dugard L. Robust stability and stabilization of uncertain linear systems with state delay: single delay case (I)[C]. Proc of IFAC Symp. Robust Control Design, Rio deJaneiro, Brazil, 1994, 469-474.
[176] Chang S S, Peng T K C. Adaptive guaranteed cost control of systems with uncertain parameters[J]. IEEE Trans. Automat. Contr, 1972,17(4): 356-361.
[177] Lin W, Dai L. Solution to the output regulation problem of linear singular systems[J]. Automatica, 1996, 32(12): 1713-1718.
[178] EI Ghaoui L, Oustry F, Ait Rami M. A cone complementarity linearization algorithm for static output-feedback and related problems[J]. IEEE Trans. Automat. Contr, 1997,42(8): 1171-1176.
[179] Xu S Y, Lam J. Robust stability and stabilization of discrete singular systems: an equivalent characterization[J]. IEEE Trans. Automat. Contr, 2004, 49(4): 568-574.
[180] Yu L, Xu J M Han Q L. Optimal guaranteed control of singular systems with delayed state and parameter uncertainties[C]. Proc of American Control Conference, 2004, 5,4811-4816.
[181] Bliman P A. Extension of Popov absolute stability criterion to non-autonomous systems with delays[J]. Int. J. Control. 2000, 73(15): 1349-1361.
[182] Xie L. Output feedback H_∞ control of systems with parameter uncertainty [J]. Int. J. Control, 1996, 63(4): 741-750.
[183] Zhang Q, Wei X, Xu J. On global exponential stability of delayed cellular neural networks with time-varying delays[J]. Appl Math Comput, 2005, 162: 679-86.
[184] Cho H J, Park J H. Novel delay-dependent robust stability criterion of delayed cellular neural networks[J]. Chaos, Solitons and Fractals, 2007,32(3): 1194-1200.
[185] Cao J D, Zhou D M. Stability analysis of delayed cellular neural networks[J]. Neural Networks, 1998, 11: 1601-1605.
[186] Han Q L, Jiang X F, Ma X. Computation of delay bound for linear neutral systems with interval time-varying discrete delay[J]. Dynnamics of Continuous, Discrete and Impulsive Systems, 2006, 13(c): 117-131.
[187] Gilbert EN. Capacity of a burst-noise channel[J]. Bell System Technical Journal, 1960, 39: 1253-1265.
[188] Elliott E O. Estimates of error rates for codes on burst-noise channels[J]. Bell System Technical Journal, 1963,42,1977-1997.
[189] Yajnik M, Moon S, Kurose J et. al. Measurement and modeling of the temporal dependence in packet loss[C]. Proc of IEEE Conference on Computer and Communications Societies, 1999, 1, 345-352.
[190] Sinopoli B, Schenato L, Franceschetti M et. al. Kalman filtering with intermittent observations[J]. IEEE Trans. Automat. Contr, 2004,49(9): 1453-1464.
[191]Ling S,Michael E,Richard M M.Towards robust control over a packet-based network[C].Proc of 17th International Symposium on Mathematical Theory of Networks and Systems,Kyoto,Japan,2006.http://www.cds.caltech.edu/-shiling/
[192]Chou M Y,Tipsuwan Y.Network-based control systems:A tutorial[C],Proc of IECON'01:27th Annu.Conf.IEEE Industrial Electronics Soc,2001,1593-1602.
[193]Sastry S S.Nonlinear systems:Analysis,Stability,and Control[M].Springer Verlag,1999.
[194]Delchamps D E Stabilizing a linear system with quantized state feedback[J],IEEE Trans.Automat.Contr,1990,35(8):916-924.
[195]Brockett R W,Liberzon D.Quantized feedback stabilization of linear systems[J].IEEE Trans.Automat.Contr,2000,45(7):1279-1289.
[196]Ishii H,Francis B A.Limited Data rate in Control Systems with Networks[M].Springer:Berlin,2002.
[197]Liberzon D.On stabilization of linear systems with limited information[J].IEEE Trans.Automat.Contr,2003,48(2):304-307.
[198]Savkin A V,Petersen I R.Set-valued state estimation via a limited capacity communication channel[J].IEEE Trans.Automat.Contr,2003,48(4):676-680.
[199]Matveev A S,Savkin A V.Multi-rate stabilization of linear multiple sensor systems via limited capacity communication channels[J].SIAM J.Control Optim,2005,44(2):584-617.
[200]Tatikonda S.Control under Communication Constrains[D].PhD thesis,IMI,Cambridge,MA,2000.
[201]宋志安,王文馨.由阶跃响应曲线辨识传递函数的图解方法[J].山东科技大学学报,2003,22(1):61-63.
[202]吴广玉.系统辨识与自适应控制[M].哈尔滨工业大学出版社,1987.
[203]郑国庆,姜立群,张玉斌.先进控制中的系统辨识问题研究[J].齐齐哈尔大学学报,2000,16(2):26-28.
[204]Limebeer D J N.The specification and purpose of a controller design case study[C].Proc of the 30th Conference on Decision and Control,Brighton,England,1991,1579-1580.