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Vol.28 No.6 崔桂梅等：网络控制系统保性能控制 .599. 0.0702 -0.9993 -0.4987 统性能指标定义成式(5)，其中Q=d击iag(1,2),R= B1= L8.42871 D- 0.9993 0.9974 0.5,对于大多数线性定常系统其解存在，K= 640 0.9992 0 E -640 ,F= 1.0×10-6×「0.0872-0.2673].仿真结果如 0 0.9996d 图3所示， 系统的初始条件集矩阵U=diag(2,2)·系 1.5 1.0m 1.5 05 1.0 0 05 0.5 -1.0 00 图3保性能鲁棒控制响应的曲线 Fig-3 Guaranteed cost robust control curves [3]俞立，不确定离散时滞系统的保性能控制。自动化学报， 4结语 2001,27(3):392 [4]樊卫华，蔡骅，陈庆伟，等.时延网络控制系统的稳定性，控 在NCS建立其具有时滯不确定的离散模型 制理论与应用，2004,21(6).880 的基础上，在网络系统时延小于一个采样周期的 [5]YuL.Gao F R.Optimal guaranteed cost control of discrete 情况下，研究了NCS的保性能鲁棒控制问题，给 time uncertain systems with both and input delays.JFranklin 出了使NCS保性能稳定的静态状态反馈控制器 Inst,338(1):101 的设计等价于求解LMI.通过仿真验证了系统具 [6]Walsh CC.Bushnell L G.Asymptotic behavior of nonlinear 有很好的鲁棒稳定性 networked control systems.IEEE Trans Autom Control. 2001,46(7):1093 参考文献 [7]陈幼平.网络化控制系统的科学问题与应用展望.控制与 决策，2004,19(9)：962 [1]Luck R.Ray A.An observer-based compensator for distributed [8]Zhang W,Branicky M S.Stability of networked control sys- delays.Automatica.1990.26(5):903 tems.IEEE Control Syst Mag.2001.2:84 [2]Woei LL.Asok R.A stochastic regulator for integrated com- [9]钟麟，王峰，MATLAB仿真技术与应用教程.北京：国防工 munication and control systems:Part I numerical analysis and 业出版社，2004 simulation.Dyn Syst Meas Control,1991.113,612 Guaranteed cost control of networked control systems CUI Guimei),MU Zhichun,LI Xicoli),HAO Zhihong? 1)Information Engineering School.University of Science and Technology Beijing.Beijing 100082.China 2)Information Engineering School,Inner Mongolia University of Science and Technology,Baotou 014010.China ABSTRACI To solve the problem of uncertain time delay in networked control systems (NCS),the un- certain of time delay was converted to the uncertainty of parameter matrixes,and the model of NCS was simplified as an uncertain discrete model with time delay.The guaranteed cost control problem for NCS was translated to a robust guaranteed cost control problem for an uncertainty discrete system with time delay based on the above model.Lyapunov theory and linear matrix inequality (LMI)were applied to prove the sufficient condition of guaranteed cost control for NCS was equivalent to solving a LMI by a static state feedback.Simulation results show effectiveness of the proposed control method. KEY WORDS networked control system;guaranteed cost control;time-delay;LMI;discrete systemB1＝ 0∙0702 8∙4287 D＝ —0∙9993 —0∙4987 0∙9993 0∙9974 E＝ 640 —640 F＝ 0∙9992 0 0 0∙9996 ． 系统的初始条件集矩阵 U＝diag（22）．系 统性能指标定义成式（5）其中 Q＝diag（12）R＝ 0∙5对于大多数线性定常系统其解存在K ＝ 1∙0×10—6×［0∙0872 —0∙2673］．仿真结果如 图3所示． 图3 保性能鲁棒控制响应的曲线 Fig．3 Guaranteed cost robust control curves 4 结语 在 NCS 建立其具有时滞不确定的离散模型 的基础上在网络系统时延小于一个采样周期的 情况下研究了 NCS 的保性能鲁棒控制问题给 出了使 NCS 保性能稳定的静态状态反馈控制器 的设计等价于求解 LMI．通过仿真验证了系统具 有很好的鲁棒稳定性． 参 考 文 献 ［1］ Luck RRay A．An observer-based compensator for distributed delays．Automatica199026（5）：903 ［2］ Woei L LAsok R．A stochastic regulator for integrated communication and control systems：Part Ⅱ numerical analysis and simulation．Dyn Syst Meas Control1991113：612 ［3］ 俞立．不确定离散时滞系统的保性能控制．自动化学报 200127（3）：392 ［4］ 樊卫华蔡骅陈庆伟等．时延网络控制系统的稳定性．控 制理论与应用200421（6）：880 ［5］ Yu LGao F R．Optimal guaranteed cost control of discrete time uncertain systems with both and input delays．J Franklin Inst338（1）：101 ［6］ Walsh G CBushnell L G．Asymptotic behavior of nonlinear networked control systems．IEEE Trans Autom Control 200146（7）：1093 ［7］ 陈幼平．网络化控制系统的科学问题与应用展望．控制与 决策200419（9）：962 ［8］ Zhang WBranicky M S．Stability of networked control systems．IEEE Control Syst Mag20012：84 ［9］ 钟麟王峰．MATLAB 仿真技术与应用教程．北京：国防工 业出版社2004 Guaranteed cost control of networked control systems CUI Guimei 12）MU Zhichun 1）LI Xiaoli 1）HAO Zhihong 2） 1） Information Engineering SchoolUniversity of Science and Technology BeijingBeijing100082China 2） Information Engineering SchoolInner Mongolia University of Science and TechnologyBaotou014010China ABSTRACT To solve the problem of uncertain time delay in networked control systems （NCS）the uncertain of time delay was converted to the uncertainty of parameter matrixesand the model of NCS was simplified as an uncertain discrete model with time delay．The guaranteed cost control problem for NCS was translated to a robust guaranteed cost control problem for an uncertainty discrete system with time delay based on the above model．Lyapunov theory and linear matrix inequality （LMI） were applied to prove the sufficient condition of guaranteed cost control for NCS was equivalent to solving a LMI by a static state feedback．Simulation results show effectiveness of the proposed control method． KEY WORDS networked control system；guaranteed cost control；time-delay；LMI；discrete system Vol．28No．6 崔桂梅等： 网络控制系统保性能控制 ·599·