网络控制系统的镇定与滤波
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摘要
在网络控制系统中,通常对象和控制器通过通信网络进行连接,该网络可能同时也为其他应用提供信息传输服务。网络控制系统的主要优点是成本低,重量轻,可靠性高,易于安装维护等。因此,网络控制系统在许多领域得到应用,如移动传感器网络、制造系统、遥操作机器人、航天系统等等。可是,引入网络会出现一些新问题:例如网络时延、数据丢包和信号量化等。本文主要针对存在网络时延和(或)数据丢包的网络控制系统,对它的分析和设计进行了深入的探讨和研究。
研究了具有随机丢包的网络控制系统的可镇定性和可检测性问题,其中随机丢包建模为当前常用的独立同分布伯努利序列。考虑了两种常用补偿丢失信号的方法:用“零信号”和用“最新收到的信号”。首先讨论了用“零信号”的网络控制系统,给出了此类网络控制系统可镇定的几个充要条件。并提出了可镇定程度的概念,它有助于进一步分析网络传输概率与网络控制系统的可镇定性之间的关系。由于镇定和检测之间的对偶性,这些结果或概念可方便地推广到网络控制系统的可检测问题。对于单输入单输出(SISO)系统,给出了保证系统可镇定或可检测所需要的最小网络传输概率的解析结果,结果表明镇定或检测同一个(SISO)系统,所需要的最小传输概率相等,并且最小传输概率只与被控对象的不稳定极点有关。从理论上证明了最小传输概率与系统的不稳定程度呈严格的正相关,即系统越不稳定,镇定或观测它所需要的传输概率越大。随后给出了用“最新收到的信号”的SISO网络控制系统可镇定的必要条件。从理论上证明了,用“最新收到的信号”补偿丢包对系统稳定性的影响不比用“零信号”的效果更好。另外,研究了基于状态观测器的状态反馈控制器在网络中最佳位置设定问题。当这类控制器配置在最佳网络节点上时,通过选择适当的控制器参数,可以使闭环系统在保证稳定的情况下,能容忍的整个网络的丢包率最大。通过仿真例子验证了所提结果的有效性。
对同时存在网络时延和数据包丢失的离散时间网络控制系统进行了稳定性分析,提出了新的时延相关的稳定判据。与现有的一些结果相比,本文提出的稳定判据主要优点是具有较低的保守性,这主要是在推导过程中利用了凸集上凸函数的性质,不需要像现有一些方法那样把时变时延和其上下界的差同时放大为时延的上下界之差,因此减少了保守性的引入。本文通过理论证明和例子比较都验证了所提稳定判据的优越性。在提出的稳定判据基础上,还给出了状态反馈控制器的设计方法。并对当前求解控制器常用的CCL算法提出了改进。最后,通过仿真示例验证了所提出的控制器设计方法也具有较低的保守性。
对于同时存在网络时延和数据包丢失的离散时间网络控制系统,提出了一种新的网络预测控制方法。和现有的网络预测控制方法相比,本文提出网络预测控制方法具有如下优点:本文方法能同时有效补偿网络时延和随机丢包的影响,利用本文方法所得到的闭环系统可镇定的条件大大降低;实现了状态反馈控制器和状态预测器满足分离原理,从而可以方便地设计保闭环系统稳定的网络预测控制器。通过理论证明和仿真例子验证了所提方法的优越性。
考虑了网络控制系统中的H∞滤波问题。在这种情形下,系统的测量信号通过存在随机时延的网络传输到滤波器,滤波器通过受到网络时延的测量信号估计系统的被估输出,这里随机时延满足独立同分布的伯努利序列。首先提出了一种新的滤波误差系统表示形式,其优点是把具有时滞状态的系统转化为无时滞的随机参数系统,从而避免利用Lyapunov-Krasovskii泛函推导系统的H∞滤波性能,减少了保守性的引入,并且证明了提出的性能分析判据比现有的结果保守性低。在滤波器的设计方法上,提出了一种新的参数化设计方法,从理论上和例子对比都验证了比现有设计方法的保守性低。另外,通过引入松弛变量的策略,又提出了进一步改进的滤波器设计方法,并通过例子进行了验证。
In a networked control system (NCS), plant and controller are typically connected via a communication network which may be shared with other applications. The main advantages of NCSs are low cost, reduced weight, simple installation and maintenance, and high reliability. Consequently, NCSs have been applied in a broad range of areas such as mobile sensor networks, manufacturing systems, teleportation of robots, aircraft systems, etc. however,the usage of the network may lead to some new problems, such as network delay, data packet loss, signal quantization, etc. In this paper, the analysis and design of networked control systems with network delay and (or) packet dropout are considered. The main contents are as follows:
Stabilizability and detectability of NCSs with random packet dropout are investigated, where the network packet-loss is modeled as an i.i.d. Bernoulli process. Two commonly used modes compensating for signal-loss—using a zero signal and using the latest available signal are compared. First NCSs with the“zero signal”mode is considered. Several necessary and sufficient conditions for stabilizablity are established. A notion of stabilizable degree is proposed, which help to further analyze the relationship between network transmission probability and stabilizability of the networked control systems. Due to the duality between stabilizability and detectability, the above results and notions about the stabilizability can readily be extended to solve the detectabiliy. For the SISO systems, an explicit formula for the least required transmission probability for the purpose of stabilizing or detecting a networked control system is derived. The result shows that the least required transmission probabilities are equal each other when stabilizing or detecting a networked control system. And it is merely dependent on the unstable poles of the system. It is theoretically validated that the least required transmission probability is strictly positive interrelated with the degree of instability of the system. That is, the more the degree of instability of a system is, the more the required transmission probability will be. Then a necessary condition for stabilizablity of NCSs with the“latest available signal”mode is proposed. It is theoretically proved that the“latest available signal”mode can not better compensate the effect of loss data than the“zero signal”one. In addition, optimizing location of state-observer based controller in the network is considered. When the controller is located the optimal node, by selecting appropriate controller parameter, the closed-loop system can be stable with maximum loss probability of the network. The efficiency of the proposed results is illustrated with some simulation examples.
The stability of the discrete-time networked control systems is analyzed when there are both network delay and packet loss in the network. A new delay-dependent stability criterion is proposed. Compared with the some existing results, the advantage of the proposed stability condition lies in its less conservativeness. Differently to pervious methods, by utilizing the properties of convex function, the differences of the delay and its upper and lower bound need not simultaneously be enlarged as the differences of its upper and lower bound. Thus the conservativeness of the result is reduced. Both theoretical proof and example show the advantage of the proposed stability criterion. Based on the stability criterion, the design method of the state-feedback controller is provided. Moreover, the CCL algorithm has been improved. Simulation example is given to show that the proposed design method of controller is also less conservativeness than the existing ones.
A new networked predictive control method is proposed for the discrete-time networked control systems, which simultaneously contain network delay and packet loss. Compared with the existing methods, the proposed method has the following merits. The proposed method can more efficiently compensate the effect of network delay and packet dropout. Thus the stabilizability condition of closed-loop systems is very easily satisfied. Moreover, by the proposed method, the state-feedback controller and state predictor can be separately designed, so the networked predictive controller can easily be design to guarantee the stability of closed-loop system. By theoretical analysis and simulation example, the advantages of the proposed method are verified.
The H∞filtering in the networked control systems is considered. Under this case, the measured signals of the system are transmitted to the filter through the network, which are inevitably subjected to the effect of the network delay. The network delays are assumed to satisafy an i.i.d. Bernoulli process. A new form of the filtering error system is proposed, which translates the delay system into a delay-free system. Therefore, Lyapunov-Krasovskii is not required when the H∞filtering performance is analyzed so that the conservativeness of result of performance analysis is reduced. Moreover, the proposed H∞performance criterion is theoretically proved that it is less conservative than the existing one. Based on this performance criterion, a new parametric design method of the filter is proposed. It also is proved that it is less conservative than the existing one. In addition, by introducing some slack variables, an improved filter design is presented and its efficiency is illustrated by an example.
研究了具有随机丢包的网络控制系统的可镇定性和可检测性问题,其中随机丢包建模为当前常用的独立同分布伯努利序列。考虑了两种常用补偿丢失信号的方法:用“零信号”和用“最新收到的信号”。首先讨论了用“零信号”的网络控制系统,给出了此类网络控制系统可镇定的几个充要条件。并提出了可镇定程度的概念,它有助于进一步分析网络传输概率与网络控制系统的可镇定性之间的关系。由于镇定和检测之间的对偶性,这些结果或概念可方便地推广到网络控制系统的可检测问题。对于单输入单输出(SISO)系统,给出了保证系统可镇定或可检测所需要的最小网络传输概率的解析结果,结果表明镇定或检测同一个(SISO)系统,所需要的最小传输概率相等,并且最小传输概率只与被控对象的不稳定极点有关。从理论上证明了最小传输概率与系统的不稳定程度呈严格的正相关,即系统越不稳定,镇定或观测它所需要的传输概率越大。随后给出了用“最新收到的信号”的SISO网络控制系统可镇定的必要条件。从理论上证明了,用“最新收到的信号”补偿丢包对系统稳定性的影响不比用“零信号”的效果更好。另外,研究了基于状态观测器的状态反馈控制器在网络中最佳位置设定问题。当这类控制器配置在最佳网络节点上时,通过选择适当的控制器参数,可以使闭环系统在保证稳定的情况下,能容忍的整个网络的丢包率最大。通过仿真例子验证了所提结果的有效性。
对同时存在网络时延和数据包丢失的离散时间网络控制系统进行了稳定性分析,提出了新的时延相关的稳定判据。与现有的一些结果相比,本文提出的稳定判据主要优点是具有较低的保守性,这主要是在推导过程中利用了凸集上凸函数的性质,不需要像现有一些方法那样把时变时延和其上下界的差同时放大为时延的上下界之差,因此减少了保守性的引入。本文通过理论证明和例子比较都验证了所提稳定判据的优越性。在提出的稳定判据基础上,还给出了状态反馈控制器的设计方法。并对当前求解控制器常用的CCL算法提出了改进。最后,通过仿真示例验证了所提出的控制器设计方法也具有较低的保守性。
对于同时存在网络时延和数据包丢失的离散时间网络控制系统,提出了一种新的网络预测控制方法。和现有的网络预测控制方法相比,本文提出网络预测控制方法具有如下优点:本文方法能同时有效补偿网络时延和随机丢包的影响,利用本文方法所得到的闭环系统可镇定的条件大大降低;实现了状态反馈控制器和状态预测器满足分离原理,从而可以方便地设计保闭环系统稳定的网络预测控制器。通过理论证明和仿真例子验证了所提方法的优越性。
考虑了网络控制系统中的H∞滤波问题。在这种情形下,系统的测量信号通过存在随机时延的网络传输到滤波器,滤波器通过受到网络时延的测量信号估计系统的被估输出,这里随机时延满足独立同分布的伯努利序列。首先提出了一种新的滤波误差系统表示形式,其优点是把具有时滞状态的系统转化为无时滞的随机参数系统,从而避免利用Lyapunov-Krasovskii泛函推导系统的H∞滤波性能,减少了保守性的引入,并且证明了提出的性能分析判据比现有的结果保守性低。在滤波器的设计方法上,提出了一种新的参数化设计方法,从理论上和例子对比都验证了比现有设计方法的保守性低。另外,通过引入松弛变量的策略,又提出了进一步改进的滤波器设计方法,并通过例子进行了验证。
In a networked control system (NCS), plant and controller are typically connected via a communication network which may be shared with other applications. The main advantages of NCSs are low cost, reduced weight, simple installation and maintenance, and high reliability. Consequently, NCSs have been applied in a broad range of areas such as mobile sensor networks, manufacturing systems, teleportation of robots, aircraft systems, etc. however,the usage of the network may lead to some new problems, such as network delay, data packet loss, signal quantization, etc. In this paper, the analysis and design of networked control systems with network delay and (or) packet dropout are considered. The main contents are as follows:
Stabilizability and detectability of NCSs with random packet dropout are investigated, where the network packet-loss is modeled as an i.i.d. Bernoulli process. Two commonly used modes compensating for signal-loss—using a zero signal and using the latest available signal are compared. First NCSs with the“zero signal”mode is considered. Several necessary and sufficient conditions for stabilizablity are established. A notion of stabilizable degree is proposed, which help to further analyze the relationship between network transmission probability and stabilizability of the networked control systems. Due to the duality between stabilizability and detectability, the above results and notions about the stabilizability can readily be extended to solve the detectabiliy. For the SISO systems, an explicit formula for the least required transmission probability for the purpose of stabilizing or detecting a networked control system is derived. The result shows that the least required transmission probabilities are equal each other when stabilizing or detecting a networked control system. And it is merely dependent on the unstable poles of the system. It is theoretically validated that the least required transmission probability is strictly positive interrelated with the degree of instability of the system. That is, the more the degree of instability of a system is, the more the required transmission probability will be. Then a necessary condition for stabilizablity of NCSs with the“latest available signal”mode is proposed. It is theoretically proved that the“latest available signal”mode can not better compensate the effect of loss data than the“zero signal”one. In addition, optimizing location of state-observer based controller in the network is considered. When the controller is located the optimal node, by selecting appropriate controller parameter, the closed-loop system can be stable with maximum loss probability of the network. The efficiency of the proposed results is illustrated with some simulation examples.
The stability of the discrete-time networked control systems is analyzed when there are both network delay and packet loss in the network. A new delay-dependent stability criterion is proposed. Compared with the some existing results, the advantage of the proposed stability condition lies in its less conservativeness. Differently to pervious methods, by utilizing the properties of convex function, the differences of the delay and its upper and lower bound need not simultaneously be enlarged as the differences of its upper and lower bound. Thus the conservativeness of the result is reduced. Both theoretical proof and example show the advantage of the proposed stability criterion. Based on the stability criterion, the design method of the state-feedback controller is provided. Moreover, the CCL algorithm has been improved. Simulation example is given to show that the proposed design method of controller is also less conservativeness than the existing ones.
A new networked predictive control method is proposed for the discrete-time networked control systems, which simultaneously contain network delay and packet loss. Compared with the existing methods, the proposed method has the following merits. The proposed method can more efficiently compensate the effect of network delay and packet dropout. Thus the stabilizability condition of closed-loop systems is very easily satisfied. Moreover, by the proposed method, the state-feedback controller and state predictor can be separately designed, so the networked predictive controller can easily be design to guarantee the stability of closed-loop system. By theoretical analysis and simulation example, the advantages of the proposed method are verified.
The H∞filtering in the networked control systems is considered. Under this case, the measured signals of the system are transmitted to the filter through the network, which are inevitably subjected to the effect of the network delay. The network delays are assumed to satisafy an i.i.d. Bernoulli process. A new form of the filtering error system is proposed, which translates the delay system into a delay-free system. Therefore, Lyapunov-Krasovskii is not required when the H∞filtering performance is analyzed so that the conservativeness of result of performance analysis is reduced. Moreover, the proposed H∞performance criterion is theoretically proved that it is less conservative than the existing one. Based on this performance criterion, a new parametric design method of the filter is proposed. It also is proved that it is less conservative than the existing one. In addition, by introducing some slack variables, an improved filter design is presented and its efficiency is illustrated by an example.
引文
[1] Walsh G C, Beldiman O, Bushnell L G. Asymptotic behavior of nonlinear networked control systems [J]. IEEE Transaction on Automatic Control. 2001, 46(7): 1093-1097.
[2] Walsh G C, Ye H, Bushnell L. Stability analysis of networked control systems [J]. IEEE Transaction on Control Systems Technology. 2002, 10(3): 438-446.
[3] Park H S, Kim Y H, Kim D S, Kwon W H. A scheduling method for network based control systems [J]. IEEE Transaction on Control Systems Technology. 2002, 10(3): 318-330.
[4] Zhivoglyadov P V, Middleton R H. Networked control design for linear systems [J]. Automatica. 2003, 39(4): 743-750.
[5] Montestruque L A, Antsaklis P J. On the model-based control of networked systems [J]. Automatica. 2003, 39(10): 1837-1843.
[6] Yang Y, Wang Y, Yang S H. Design of a networked control system with random transmission delay and uncertain process parameters [J]. International Journal of Systems Science. 2008, 39(11): 1065-1074.
[7] Raji R S. Smart network for control [J]. IEEE Spectrum. 1994, 49-55.
[8]理查德M.穆拉里编著,陈虹,马彦译.信息爆炸时代的控制.北京:科学出版社. 2004.
[9] Lian F L, Moyne J R, Tilbury D M. Performance evaluation of control networks: Ethernet, ControlNet and DeviceNet [J]. IEEE Control Systems Magazine. 2001, 66-83
[10] Matveev A S, Savkin A V. Estimation and control over communication networks. Boston: Birkh?user. 2009.
[11] Halevi Y, Ray, A. Integrated communication and control systems: part I—analysis [J]. Journal of Dynamic Systems, Measurement, and Control. 1988, 110, 367-373.
[12] Ray A, Halevi Y. Integrated communication and control systems: part II—design considerations [J]. Journal of Dynamic Systems, Measurement, and Control.1988, 110, 374-381.
[13] Liou L W, Ray A. Integrated communication and control systems: part III—nonidentical sensor and controller sampling [J]. Journal of Dynamic Systems, Measurement, and Control. 1990. 112, 357-364.
[14] Bushnell L G. Networks and control [J]. IEEE Control Systems Magazine. 2001. 21(1): 22-23
[15] Antsaklis P, Baillieul J. Guest editorial Special issue on networked control systems [J]. IEEE Transaction on Automatic Control. 2004. 49(9): 1421-1423.
[16] Antsaklis P, Baillieul J. Special issue on technology of networked control systems [J]. Proceedings of the IEEE. 2007. 95(1): 5-8
[17] Zhang W, Branicky M S, Phillips S M. Stability of networked control systems [J]. IEEE Control Systems Magazine. 2001, 84-99.
[18] Hassibi A, Boyd S P, How J P. Control of asynchronous dynamical systems with rate constraints on events [C]. Proceedings of the 38th IEEE Conference on Decision and Control. Phoenix, AZ. 1999, 1345-1351.
[19] Zhang W A, Yu L. Output feedback stabilization of networked control systems with packet dropouts [J]. IEEE Transactions on Automatic Control. 2007, 52(9): 1705-1710.
[20] Huang M, Dey S. Stability of Kalman filtering with Markovian packet losses [J]. Automatica, 2007, 43(4): 598-607.
[21] Smith S, Seiler P. Estimation with lossy measurements: jump estimators for jump systems [J]. IEEE Transactions on Automatic Control. 2003, 48(12): 2163-2171.
[22] Azimi-sadjadi B. Stability of networked control systems in the presence of packet losses [C]. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA. 2003, 676-681.
[23] Imer O C, Yuksel S, Basar T. Optimal control of LTI systems over unreliable communication links [J]. Automatica. 2006, 42(9): 1429-1439.
[24] Gupta V, Hassibi B, Murray M R. Optimal LQG control across packet-dropping links [J]. Systems & Control Letters. 2007, 56(6): 439-446.
[25] Seiler P, Sengupta R. An H∞approach to networked control [J]. IEEE Transactions on Automatic Control. 2005, 50(3): 356-364.
[26] Nahi, N E. Optimal recursive estimation with uncertain observation. IEEE Transactions on Information Theory. 1969, 15(4): 457-462.
[27] Wang Y, Ho D, Liu X. Variance-constrained filtering for uncertain stochastic systems with missing measurements [J]. IEEE Transactions Automatic Control. 2003, 48(7): 1254-1258.
[28] Fortmann T, Bar-Shalom Y, Scheffe M, Gelfand S. Detection thresholds for tracking in clutter—a connection between estimation and signal processing [J]. IEEE Transactions on Automatic Control. 1985, 30(3): 221-229.
[29] Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations [J]. IEEE Transactions on Automatic Control. 2004, 49(9): 1453-1464.
[30] Epstein M, Shi L, Tiwari A, Murray R M. Probabilistic performance of state estimation across a lossy network [J]. Automatica, 2008, 44(12): 3046-3053.
[31] Plarre K, Bullo F. On Kalman filtering for detectable systems with intermittent observations [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 386-390.
[32] Sun S, Xie L, Xiao W, Soh Y C. Optimal linear estimation for systems with multiple packet dropouts [J]. Automatica, 2008, 44(5): 1333-1342.
[33] Mostofi Y, Murray R M. To drop or not to drop: design principles for Kalman filtering over wireless fading Channels [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 376-381.
[34] Sahebsara M, Chen T, Shah S L. Optimal H2 filtering in networked control systems with multiple packet dropout [J]. IEEE Transactions on Automatic Control. 2007, 52(8): 1508-1513.
[35] Sahebsara M, Chen T, Shah S L. Optimal H∞filtering in networked control systems with multiple packet dropouts [J]. Systems & Control Letters. 2008, 57(9):696-702.
[36] Yu M, Wang L, Chu T, et al. Stabilization of networked control systems with data packet dropout and networked delays via switching system approach [C]. Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas. 2004, 3539-3544.
[37] Xiong J, Lam J. Stabilization of linear systems over networks with bounded packet loss [J]. Automatica. 2007, 43(1): 80-87.
[38] Wu J, Chen T. Design of networked control systems with packet dropouts [J]. IEEE Transactions on Automatic Control. 2007, 52(7): 1314-1319.
[39] Hu S, Yan W Y. Stability robustness of networked control systems with respectto packet loss [J]. Automatica. 2007, 43(7): 1243-1248.
[40] Hadjicostis C N, Touri R. Feedback control utilizing packet dropping network links [C]. Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA. 2002, 1205-1210.
[41] Munoz de la P D, Christofides P D. Lyapunov-based model predictive control of nonlinear systems subject to data losses [J]. IEEE Transactions on Automatic Control. 2008, 53(9): 2076-2089.
[42] Montestruque L A, Antsaklis P J. Stability of model-based networked control systems with time-varying transmission times [J]. IEEE Transaction on Automatic Control. 2004, 49(9): 1562-1572.
[43] Mastellone S, Abdallah C T, Dorato P. Model-based networked control for nonlinear systems with stochastic packet dropout [C]. American Control Conference, Portland, OR, USA. 2005, 2365-2370.
[44] Qiang L, Lemmon M D. Power spectral analysis of networked control systems with data dropouts [J]. IEEE Transactions on Automatic Control. 2004, 49(6): 955-959.
[45] Tian Y C, Levy D. Compensation for control packet dropout in networked control systems [J]. Information Sciences. 2008, 178(5): 1263-1278.
[46] Luck R, Ray A. An observe-based compensator for distributed delays [J]. Automatica. 1990, 26(5): 903-908.
[47] Luck R, Ray A. Experimental verification of a delay compensation algorithm for integrated communication and control systems [J]. International Journal of Control. 1994, 59(6): 1357-1372.
[48] Zhang L, Shi Y, Chen T, Huang B. A new method for stabilization of networked control systems with random delays [J]. IEEE Transactions on Automatic Control. 2005, 50(8): 1177-1181.
[49] Zhang W A, Yu L. Modelling and control of networked control systems with both network-induced delay and packet-dropout [J]. Automatica, 2008, 44(12): 3206-3210.
[50] Nilsson J, Bernhardsson B, Wittenmark B. Stochastic analysis and control of real-time sytems with random time delays [J]. Automatica, 1998. 34(1):57-64.
[51] Nilsson J. Real-time control systems with delays. Ph. D. dissertation. Department of Automatic Control. Lund Institute of Technology, Lund, Sweden. January 1998.
[52] Hu S, Zhu Q. Stochastic optimal control and analysis of stability of networked control systems with long delay [J]. Automatica. 2003, 39():1877-1884.
[53] Lin H, Zhai G S, Antasklis P J. Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach [J]. International Journal of Control. 2005, 78(18): 1447-1458.
[54] Yue D, Han Q L, Peng C. State feedback controller design of networked control systems [J]. IEEE Transaction on Circuits and Systems II: Express Briefs. 2004, 51(11): 640-644.
[55] Yue D, Han Q L, Lam J. Network-based robust H∞control of systems with uncertainty [J]. Automatica. 2005, 41(6): 999-1007.
[56] Kim D S, Lee Y S, Kwon W H, Park H S. Maximum allowable delay bounds of networked control systems [J]. Control Engineering Practice, 2003, 11(11):1301-1313.
[57] Gao H, Chen T. H∞Estimation for uncertain systems with limited communication capacity [J]. IEEE Transactions on Automatic Control. 2007, 52(11): 2070-2084.
[58] Gao H, Chen T, Chai T. Passivity and passification for networked control systems [J]. SIAM Journal on Control and Optimization. 2007, 46(4): 1299-1322.
[59] Gao H, Chen T, Lam J. A new delay system approach to network-based control [J]. Automatica. 2008, 44(1): 39-52.
[60] Gao H, Chen T. Network-based H∞output tracking control [J]. IEEE Transactions on Automatic Control. 2008, 53(3): 655-667.
[61] He Y, Liu G P, Rees D, Wu M. Improved stabilisation method for networked control systems [J]. IET Control Theory and Applications. 2007, 1(6): 1580-1585.
[62] Jiang X, Han Q L, Liu S, Xue A. A new H∞stabilization criterion for networked control systems [J]. IEEE Transactions on Automatic Control. 2008, 53(4): 1025-1032.
[63] Lin C, Wang Z, Yang F. Observer-based networked control for continuous-time systems with random sensor delays [J]. Automatica. 2009, 45(2): 578-584.
[64] Xiong J, Lam J. Stabilization of networked control systems with a logic ZOH [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 358-363.
[65] Gao H, Meng X, Chen T. Stabilization of networked control systems with a newdelay characterization [J]. IEEE Transactions on Automatic Control. 2008, 53(9): 2142-2148.
[66] Zhou S, Feng G. H∞filtering for discrete-time systems with randomly varying sensor delays [J]. Automatica, 2008, 44(7):1918-1922.
[67] Ray A. Output feedback control under randomly varying delays [J]. Journal of Guidance Control and Dynamics. 1994, 17(4): 701-711.
[68] Guo Y, Li S. Comments and improved results on“H∞filtering for discrete-time systems with randomly varying sensor delays”[J]. Automatica. 2009, 45(7): 1784-1787.
[69] Liu G P, Mu J X, Rees D, Chai S C. Design and stability analysis of networked control systems with random communication time delay using the modified MPC [J]. International Journal of Control. 2006, 79(4):288-297.
[70] Liu G P, Xia Y, Rees D, Hu W. Design and stability criteria of networked predictive control systems with random networked delay in the feedback channel [J]. IEEE Transactions on Systems, Man, and Cybernetics—Part C: Applications and reviews. 2007, 37(2):173-184.
[71] Liu G P, Xia Y, Chen J, Rees D, Hu W. Networked predictive control of systems with random network delays in both forward and feedback channels [J]. IEEE Transactions on Industrial Electronics. 2007, 54(3): 1282-1297.
[72] Hu W, Liu G P, Rees D. Event-driven networked predictive control [J]. IEEE Transactions on Industrial Electronics. 2007, 54(3): 1603-1613.
[73] Hu W, Liu G P, Rees D. Networked predictive control over the internet using round-trip delay measurement [J]. IEEE Transactions on Instrumentation and Measurement. 2008, 57(10): 2231-2241.
[74] Zhao Y B, Liu G P, Rees D. Networked predictive control systems based on the Hammerstein model [J]. IEEE Transactions on Circuits and Systems—II: Express Briefs. 2008, 55(5): 469-473.
[75] Zhao Y B, Liu G P, Rees D. A predictive control-based approach to networked Hammerstein systems: design and stability analysis [J]. IEEE Transactions on Systems, Man, and cybernetics—Part B: Cybernetics. 2008, 38(3): 700-708.
[76] Ji Y, Chizeck H J, Feng X, Loparo K A. Stability and control of discrete-time jump linear systems [J]. Control Theory and Advanced Technology. 1991, 7(2): 247-270.
[77]俞立.鲁棒控制.北京:清华大学出版社. 2002: 8-9.
[78] Feng J, Lam J, Xu S, Shu Z. Optimal stabilizing controllers for linear discrete-time stochastic systems [J]. Optimal Control Applications and Methods. 2008, 29(3): 243-253.
[79] Feng J. Xu S. Robust H∞control with maximal decay rate for linear discrete-time stochastic systems [J]. Journal of Mathematical Analysis and Applications. 2009, 353(1): 460-469.
[80] Elia N, Mitter S. Stabilization of linear systems with limited information. IEEE Transactions on Automatic Control. 2001, 46(9): 1384-1400.
[81] Boyd S, Ghaoui L E, Feron E, Balakrishnan V. Linear matrix inequlities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics. 1994.
[82] Kwakemaak H, Sivan R. Linear optimal control systems. New York: Wiley. 1972.
[83] Elia N. When bode meets Shannon: control-oriented feedback communication schemes. IEEE Transaction Automatic Control. 2004, 49(9): 1477-1488.
[84] Robinson C L, Kumar P R. Optimizing controller location in networked control systems with packet drops [J]. IEEE Journal on Selected Areas in Communications. 2008, 26(4): 661-671.
[85] Gao H, Chen T. New results on stability of discrete-time systems with time-varying state delay [J]. IEEE Transactions on Automatic Control. 2007, 52(2): 328-334.
[86] Xu S, Chen T. Robust H∞control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers [J]. Systems & Control Letters. 2004, 51(3):171-183.
[87] Gao H, Lam J, Wang C, Wang Y. Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay [J]. IEE Proceedings-Control Theory and Applications. 2004, 151(6): 691-698.
[88] Fridman E, Shaked U. Stability and guaranteed cost control of uncertain discrete delay systems [J]. International Journal of Control. 2005, 78(4): 235-246.
[89] Jiang X, Hang Q L, Yu X. Stability criteria for linear discrete-time systems with interval-like time-varying delay [C]. Proceedings of the American Control Conference, IEEE, Protland, OR, USA. 2005: 2817-2822.
[90] Zhang B, Xu S, Zou Y. Improved stability criterion and its application in delayed controller design for discrete-time systems [J]. Automatica. 2008, 44(11):2963-2967.
[91] Peaucelle D, Gouaisbaut F. Discussion on:‘Parameter-dependent Lyapunov function approach to stability analysis and design for uncertain systems with time-varying delay’[J]. European Journal of Control. 2005, 11(1): 69-70.
[92] Ghaoui L E, Oustry F, AitRami M. A cone complementarity linearization algorithm for state output-feedback and related problems [J]. IEEE Transations on Automatic Control. 1997, 42(8): 1171-1176.
[93] Gu K. An integral inequality in the stability problem of time-delay systems [C]. Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia. 2000, 2805-2810.
[94] Naghshtabrizi P, Hespanha J, Teel A. On the robust stability and stabilization of sampled-data systems: A hybird system approach [C]. Proceedings of 45th IEEE Conference on Decision and Control, San Diego, USA. 2006, 4873-4878.
[95] Yu M, Wang L, Chu T, Hao F. An LMI approach to networked control systems with data packet dropout and transmission delays [C]. Proceedings of the 43rd Conference on Decision and Control, Altantis, Paradise Island, Bahamas. 2004, 3545-3540.
[96] Shao H. Improved delay-dependent stability criteria for systems with a delay varying in a range. Automatica. 2008, 44(12): 3215-3218.
[97] Tian E. G, Yue D, Zhang Y. J, Peng C. Improved stability analysis for discrete systems with interval time-varying delay [C]. Proceeding of the 27th Chinese Control Conference, Kunming, China. 2008, 86-90.
[98] Lam J, Gao H, Wang C. Stability analysis for continuous systems with two additive time-varying delay components [J]. Systems & Control Letters, 2007, 56(1): 16-24.
[99] Quevedo D E, Silva E I, Goodwin G C. Packetized predictive control over erasure channels [C]. Proceedings of the American Control Conference, IEEE, New York City, USA. 2007, 1003-1008.
[100] Fantoni I, Lozano R. Non-linear control for underactuated mechanical systems. UK: Springer. 2002.
[101] Shi P, Boukas E K, Agarwal R K. Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters [J]. IEEE Transactions on Automatic Control. 1999, 44(8): 1592-1597.
[102] Qi H, Moore J B. Direct Kalman filtering approach for GPS/INS integrationg [J].IEEE Transaction on Aerospace and Electronic Systems. 2002, 38(2): 687-693.
[103] Barbosa K A, de Souza C E, Trofino A. Robust H2 filtering for uncertain linear systems: LMI based method with parametric Lyapunov functions [J]. Systems & Control Letters. 2005, 54(): 251-262.
[104] Lee K H, Hang B. Robust H 2 filtering for continous-time stochastic systems with polytopic parameter uncertainty [J]. Automatica, 2008, 44(10): 2686-2690.
[105] Elsayed A, Grimble M. A new approach to H∞design for optimal digital linear filter [J]. IMA Journal of Mathematical Control and Infromation. 1989, 6(3): 233-251.
[106] Xie L, Liu L, Zhang D, Zhang H. Improved H2 and H∞filtering for uncertain discrete-time systems [J]. Automatica. 40(5): 873-880.
[107] Gao H, Wang C. A delay-dependent approach to robust H∞filtering for uncertain discrete-time state-delayed systems [J]. IEEE Transactions on Signal Processing. 2004, 52(6): 1631-1640.
[108] Yue D, Han Q L. Robust H∞filter design of uncertain descriptor systems with discrete and distributed delays [J]. IEEE Transaction on Signal Processing. 2004, 52(11): 3200-3212.
[109] de Souza C E, Trofino A, Barbosa K A. Mode-independent H∞for Markovian jump linear systems [J]. IEEE Transactions on Automatic Control. 2006, 51(11): 1837-1841.
[110] Yang G H, Che W W. Non-fragile H∞filter design for linear continuous-time systems [J]. Automatica. 2008, 44(11): 2849-2856.
[111] Palhares, R M. de Souza C E, Peres P L D. Robust H∞filtering for uncertain discrete-time state-delayed systems [J]. IEEE Transactions on Signal Process. 2001, 49(8): 1696-1703.
[112] Yaz E, Ray A. Linear unbiased state estimation under randomly varying bounded sensor delay [J]. Applied Mathematics Letters. 1998, 11(4): 27-32.
[113] Wang Z, Ho D W C, Liu X. Robust filtering under randomly varying sensor delay with variance constraints [J]. IEEE Transactions on Circuits and Systems II: Express Briefs. 2004, 51(6): 320-326.
[114] Yang F W, Wang Z, Huang Y S, Gani M. H∞control for networked systems with random communication delays [J]. IEEE Transactions on Automatic Control. 2006, 51(3): 511-518.
[2] Walsh G C, Ye H, Bushnell L. Stability analysis of networked control systems [J]. IEEE Transaction on Control Systems Technology. 2002, 10(3): 438-446.
[3] Park H S, Kim Y H, Kim D S, Kwon W H. A scheduling method for network based control systems [J]. IEEE Transaction on Control Systems Technology. 2002, 10(3): 318-330.
[4] Zhivoglyadov P V, Middleton R H. Networked control design for linear systems [J]. Automatica. 2003, 39(4): 743-750.
[5] Montestruque L A, Antsaklis P J. On the model-based control of networked systems [J]. Automatica. 2003, 39(10): 1837-1843.
[6] Yang Y, Wang Y, Yang S H. Design of a networked control system with random transmission delay and uncertain process parameters [J]. International Journal of Systems Science. 2008, 39(11): 1065-1074.
[7] Raji R S. Smart network for control [J]. IEEE Spectrum. 1994, 49-55.
[8]理查德M.穆拉里编著,陈虹,马彦译.信息爆炸时代的控制.北京:科学出版社. 2004.
[9] Lian F L, Moyne J R, Tilbury D M. Performance evaluation of control networks: Ethernet, ControlNet and DeviceNet [J]. IEEE Control Systems Magazine. 2001, 66-83
[10] Matveev A S, Savkin A V. Estimation and control over communication networks. Boston: Birkh?user. 2009.
[11] Halevi Y, Ray, A. Integrated communication and control systems: part I—analysis [J]. Journal of Dynamic Systems, Measurement, and Control. 1988, 110, 367-373.
[12] Ray A, Halevi Y. Integrated communication and control systems: part II—design considerations [J]. Journal of Dynamic Systems, Measurement, and Control.1988, 110, 374-381.
[13] Liou L W, Ray A. Integrated communication and control systems: part III—nonidentical sensor and controller sampling [J]. Journal of Dynamic Systems, Measurement, and Control. 1990. 112, 357-364.
[14] Bushnell L G. Networks and control [J]. IEEE Control Systems Magazine. 2001. 21(1): 22-23
[15] Antsaklis P, Baillieul J. Guest editorial Special issue on networked control systems [J]. IEEE Transaction on Automatic Control. 2004. 49(9): 1421-1423.
[16] Antsaklis P, Baillieul J. Special issue on technology of networked control systems [J]. Proceedings of the IEEE. 2007. 95(1): 5-8
[17] Zhang W, Branicky M S, Phillips S M. Stability of networked control systems [J]. IEEE Control Systems Magazine. 2001, 84-99.
[18] Hassibi A, Boyd S P, How J P. Control of asynchronous dynamical systems with rate constraints on events [C]. Proceedings of the 38th IEEE Conference on Decision and Control. Phoenix, AZ. 1999, 1345-1351.
[19] Zhang W A, Yu L. Output feedback stabilization of networked control systems with packet dropouts [J]. IEEE Transactions on Automatic Control. 2007, 52(9): 1705-1710.
[20] Huang M, Dey S. Stability of Kalman filtering with Markovian packet losses [J]. Automatica, 2007, 43(4): 598-607.
[21] Smith S, Seiler P. Estimation with lossy measurements: jump estimators for jump systems [J]. IEEE Transactions on Automatic Control. 2003, 48(12): 2163-2171.
[22] Azimi-sadjadi B. Stability of networked control systems in the presence of packet losses [C]. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA. 2003, 676-681.
[23] Imer O C, Yuksel S, Basar T. Optimal control of LTI systems over unreliable communication links [J]. Automatica. 2006, 42(9): 1429-1439.
[24] Gupta V, Hassibi B, Murray M R. Optimal LQG control across packet-dropping links [J]. Systems & Control Letters. 2007, 56(6): 439-446.
[25] Seiler P, Sengupta R. An H∞approach to networked control [J]. IEEE Transactions on Automatic Control. 2005, 50(3): 356-364.
[26] Nahi, N E. Optimal recursive estimation with uncertain observation. IEEE Transactions on Information Theory. 1969, 15(4): 457-462.
[27] Wang Y, Ho D, Liu X. Variance-constrained filtering for uncertain stochastic systems with missing measurements [J]. IEEE Transactions Automatic Control. 2003, 48(7): 1254-1258.
[28] Fortmann T, Bar-Shalom Y, Scheffe M, Gelfand S. Detection thresholds for tracking in clutter—a connection between estimation and signal processing [J]. IEEE Transactions on Automatic Control. 1985, 30(3): 221-229.
[29] Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations [J]. IEEE Transactions on Automatic Control. 2004, 49(9): 1453-1464.
[30] Epstein M, Shi L, Tiwari A, Murray R M. Probabilistic performance of state estimation across a lossy network [J]. Automatica, 2008, 44(12): 3046-3053.
[31] Plarre K, Bullo F. On Kalman filtering for detectable systems with intermittent observations [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 386-390.
[32] Sun S, Xie L, Xiao W, Soh Y C. Optimal linear estimation for systems with multiple packet dropouts [J]. Automatica, 2008, 44(5): 1333-1342.
[33] Mostofi Y, Murray R M. To drop or not to drop: design principles for Kalman filtering over wireless fading Channels [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 376-381.
[34] Sahebsara M, Chen T, Shah S L. Optimal H2 filtering in networked control systems with multiple packet dropout [J]. IEEE Transactions on Automatic Control. 2007, 52(8): 1508-1513.
[35] Sahebsara M, Chen T, Shah S L. Optimal H∞filtering in networked control systems with multiple packet dropouts [J]. Systems & Control Letters. 2008, 57(9):696-702.
[36] Yu M, Wang L, Chu T, et al. Stabilization of networked control systems with data packet dropout and networked delays via switching system approach [C]. Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas. 2004, 3539-3544.
[37] Xiong J, Lam J. Stabilization of linear systems over networks with bounded packet loss [J]. Automatica. 2007, 43(1): 80-87.
[38] Wu J, Chen T. Design of networked control systems with packet dropouts [J]. IEEE Transactions on Automatic Control. 2007, 52(7): 1314-1319.
[39] Hu S, Yan W Y. Stability robustness of networked control systems with respectto packet loss [J]. Automatica. 2007, 43(7): 1243-1248.
[40] Hadjicostis C N, Touri R. Feedback control utilizing packet dropping network links [C]. Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA. 2002, 1205-1210.
[41] Munoz de la P D, Christofides P D. Lyapunov-based model predictive control of nonlinear systems subject to data losses [J]. IEEE Transactions on Automatic Control. 2008, 53(9): 2076-2089.
[42] Montestruque L A, Antsaklis P J. Stability of model-based networked control systems with time-varying transmission times [J]. IEEE Transaction on Automatic Control. 2004, 49(9): 1562-1572.
[43] Mastellone S, Abdallah C T, Dorato P. Model-based networked control for nonlinear systems with stochastic packet dropout [C]. American Control Conference, Portland, OR, USA. 2005, 2365-2370.
[44] Qiang L, Lemmon M D. Power spectral analysis of networked control systems with data dropouts [J]. IEEE Transactions on Automatic Control. 2004, 49(6): 955-959.
[45] Tian Y C, Levy D. Compensation for control packet dropout in networked control systems [J]. Information Sciences. 2008, 178(5): 1263-1278.
[46] Luck R, Ray A. An observe-based compensator for distributed delays [J]. Automatica. 1990, 26(5): 903-908.
[47] Luck R, Ray A. Experimental verification of a delay compensation algorithm for integrated communication and control systems [J]. International Journal of Control. 1994, 59(6): 1357-1372.
[48] Zhang L, Shi Y, Chen T, Huang B. A new method for stabilization of networked control systems with random delays [J]. IEEE Transactions on Automatic Control. 2005, 50(8): 1177-1181.
[49] Zhang W A, Yu L. Modelling and control of networked control systems with both network-induced delay and packet-dropout [J]. Automatica, 2008, 44(12): 3206-3210.
[50] Nilsson J, Bernhardsson B, Wittenmark B. Stochastic analysis and control of real-time sytems with random time delays [J]. Automatica, 1998. 34(1):57-64.
[51] Nilsson J. Real-time control systems with delays. Ph. D. dissertation. Department of Automatic Control. Lund Institute of Technology, Lund, Sweden. January 1998.
[52] Hu S, Zhu Q. Stochastic optimal control and analysis of stability of networked control systems with long delay [J]. Automatica. 2003, 39():1877-1884.
[53] Lin H, Zhai G S, Antasklis P J. Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach [J]. International Journal of Control. 2005, 78(18): 1447-1458.
[54] Yue D, Han Q L, Peng C. State feedback controller design of networked control systems [J]. IEEE Transaction on Circuits and Systems II: Express Briefs. 2004, 51(11): 640-644.
[55] Yue D, Han Q L, Lam J. Network-based robust H∞control of systems with uncertainty [J]. Automatica. 2005, 41(6): 999-1007.
[56] Kim D S, Lee Y S, Kwon W H, Park H S. Maximum allowable delay bounds of networked control systems [J]. Control Engineering Practice, 2003, 11(11):1301-1313.
[57] Gao H, Chen T. H∞Estimation for uncertain systems with limited communication capacity [J]. IEEE Transactions on Automatic Control. 2007, 52(11): 2070-2084.
[58] Gao H, Chen T, Chai T. Passivity and passification for networked control systems [J]. SIAM Journal on Control and Optimization. 2007, 46(4): 1299-1322.
[59] Gao H, Chen T, Lam J. A new delay system approach to network-based control [J]. Automatica. 2008, 44(1): 39-52.
[60] Gao H, Chen T. Network-based H∞output tracking control [J]. IEEE Transactions on Automatic Control. 2008, 53(3): 655-667.
[61] He Y, Liu G P, Rees D, Wu M. Improved stabilisation method for networked control systems [J]. IET Control Theory and Applications. 2007, 1(6): 1580-1585.
[62] Jiang X, Han Q L, Liu S, Xue A. A new H∞stabilization criterion for networked control systems [J]. IEEE Transactions on Automatic Control. 2008, 53(4): 1025-1032.
[63] Lin C, Wang Z, Yang F. Observer-based networked control for continuous-time systems with random sensor delays [J]. Automatica. 2009, 45(2): 578-584.
[64] Xiong J, Lam J. Stabilization of networked control systems with a logic ZOH [J]. IEEE Transactions on Automatic Control. 2009, 54(2): 358-363.
[65] Gao H, Meng X, Chen T. Stabilization of networked control systems with a newdelay characterization [J]. IEEE Transactions on Automatic Control. 2008, 53(9): 2142-2148.
[66] Zhou S, Feng G. H∞filtering for discrete-time systems with randomly varying sensor delays [J]. Automatica, 2008, 44(7):1918-1922.
[67] Ray A. Output feedback control under randomly varying delays [J]. Journal of Guidance Control and Dynamics. 1994, 17(4): 701-711.
[68] Guo Y, Li S. Comments and improved results on“H∞filtering for discrete-time systems with randomly varying sensor delays”[J]. Automatica. 2009, 45(7): 1784-1787.
[69] Liu G P, Mu J X, Rees D, Chai S C. Design and stability analysis of networked control systems with random communication time delay using the modified MPC [J]. International Journal of Control. 2006, 79(4):288-297.
[70] Liu G P, Xia Y, Rees D, Hu W. Design and stability criteria of networked predictive control systems with random networked delay in the feedback channel [J]. IEEE Transactions on Systems, Man, and Cybernetics—Part C: Applications and reviews. 2007, 37(2):173-184.
[71] Liu G P, Xia Y, Chen J, Rees D, Hu W. Networked predictive control of systems with random network delays in both forward and feedback channels [J]. IEEE Transactions on Industrial Electronics. 2007, 54(3): 1282-1297.
[72] Hu W, Liu G P, Rees D. Event-driven networked predictive control [J]. IEEE Transactions on Industrial Electronics. 2007, 54(3): 1603-1613.
[73] Hu W, Liu G P, Rees D. Networked predictive control over the internet using round-trip delay measurement [J]. IEEE Transactions on Instrumentation and Measurement. 2008, 57(10): 2231-2241.
[74] Zhao Y B, Liu G P, Rees D. Networked predictive control systems based on the Hammerstein model [J]. IEEE Transactions on Circuits and Systems—II: Express Briefs. 2008, 55(5): 469-473.
[75] Zhao Y B, Liu G P, Rees D. A predictive control-based approach to networked Hammerstein systems: design and stability analysis [J]. IEEE Transactions on Systems, Man, and cybernetics—Part B: Cybernetics. 2008, 38(3): 700-708.
[76] Ji Y, Chizeck H J, Feng X, Loparo K A. Stability and control of discrete-time jump linear systems [J]. Control Theory and Advanced Technology. 1991, 7(2): 247-270.
[77]俞立.鲁棒控制.北京:清华大学出版社. 2002: 8-9.
[78] Feng J, Lam J, Xu S, Shu Z. Optimal stabilizing controllers for linear discrete-time stochastic systems [J]. Optimal Control Applications and Methods. 2008, 29(3): 243-253.
[79] Feng J. Xu S. Robust H∞control with maximal decay rate for linear discrete-time stochastic systems [J]. Journal of Mathematical Analysis and Applications. 2009, 353(1): 460-469.
[80] Elia N, Mitter S. Stabilization of linear systems with limited information. IEEE Transactions on Automatic Control. 2001, 46(9): 1384-1400.
[81] Boyd S, Ghaoui L E, Feron E, Balakrishnan V. Linear matrix inequlities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics. 1994.
[82] Kwakemaak H, Sivan R. Linear optimal control systems. New York: Wiley. 1972.
[83] Elia N. When bode meets Shannon: control-oriented feedback communication schemes. IEEE Transaction Automatic Control. 2004, 49(9): 1477-1488.
[84] Robinson C L, Kumar P R. Optimizing controller location in networked control systems with packet drops [J]. IEEE Journal on Selected Areas in Communications. 2008, 26(4): 661-671.
[85] Gao H, Chen T. New results on stability of discrete-time systems with time-varying state delay [J]. IEEE Transactions on Automatic Control. 2007, 52(2): 328-334.
[86] Xu S, Chen T. Robust H∞control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers [J]. Systems & Control Letters. 2004, 51(3):171-183.
[87] Gao H, Lam J, Wang C, Wang Y. Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay [J]. IEE Proceedings-Control Theory and Applications. 2004, 151(6): 691-698.
[88] Fridman E, Shaked U. Stability and guaranteed cost control of uncertain discrete delay systems [J]. International Journal of Control. 2005, 78(4): 235-246.
[89] Jiang X, Hang Q L, Yu X. Stability criteria for linear discrete-time systems with interval-like time-varying delay [C]. Proceedings of the American Control Conference, IEEE, Protland, OR, USA. 2005: 2817-2822.
[90] Zhang B, Xu S, Zou Y. Improved stability criterion and its application in delayed controller design for discrete-time systems [J]. Automatica. 2008, 44(11):2963-2967.
[91] Peaucelle D, Gouaisbaut F. Discussion on:‘Parameter-dependent Lyapunov function approach to stability analysis and design for uncertain systems with time-varying delay’[J]. European Journal of Control. 2005, 11(1): 69-70.
[92] Ghaoui L E, Oustry F, AitRami M. A cone complementarity linearization algorithm for state output-feedback and related problems [J]. IEEE Transations on Automatic Control. 1997, 42(8): 1171-1176.
[93] Gu K. An integral inequality in the stability problem of time-delay systems [C]. Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia. 2000, 2805-2810.
[94] Naghshtabrizi P, Hespanha J, Teel A. On the robust stability and stabilization of sampled-data systems: A hybird system approach [C]. Proceedings of 45th IEEE Conference on Decision and Control, San Diego, USA. 2006, 4873-4878.
[95] Yu M, Wang L, Chu T, Hao F. An LMI approach to networked control systems with data packet dropout and transmission delays [C]. Proceedings of the 43rd Conference on Decision and Control, Altantis, Paradise Island, Bahamas. 2004, 3545-3540.
[96] Shao H. Improved delay-dependent stability criteria for systems with a delay varying in a range. Automatica. 2008, 44(12): 3215-3218.
[97] Tian E. G, Yue D, Zhang Y. J, Peng C. Improved stability analysis for discrete systems with interval time-varying delay [C]. Proceeding of the 27th Chinese Control Conference, Kunming, China. 2008, 86-90.
[98] Lam J, Gao H, Wang C. Stability analysis for continuous systems with two additive time-varying delay components [J]. Systems & Control Letters, 2007, 56(1): 16-24.
[99] Quevedo D E, Silva E I, Goodwin G C. Packetized predictive control over erasure channels [C]. Proceedings of the American Control Conference, IEEE, New York City, USA. 2007, 1003-1008.
[100] Fantoni I, Lozano R. Non-linear control for underactuated mechanical systems. UK: Springer. 2002.
[101] Shi P, Boukas E K, Agarwal R K. Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters [J]. IEEE Transactions on Automatic Control. 1999, 44(8): 1592-1597.
[102] Qi H, Moore J B. Direct Kalman filtering approach for GPS/INS integrationg [J].IEEE Transaction on Aerospace and Electronic Systems. 2002, 38(2): 687-693.
[103] Barbosa K A, de Souza C E, Trofino A. Robust H2 filtering for uncertain linear systems: LMI based method with parametric Lyapunov functions [J]. Systems & Control Letters. 2005, 54(): 251-262.
[104] Lee K H, Hang B. Robust H 2 filtering for continous-time stochastic systems with polytopic parameter uncertainty [J]. Automatica, 2008, 44(10): 2686-2690.
[105] Elsayed A, Grimble M. A new approach to H∞design for optimal digital linear filter [J]. IMA Journal of Mathematical Control and Infromation. 1989, 6(3): 233-251.
[106] Xie L, Liu L, Zhang D, Zhang H. Improved H2 and H∞filtering for uncertain discrete-time systems [J]. Automatica. 40(5): 873-880.
[107] Gao H, Wang C. A delay-dependent approach to robust H∞filtering for uncertain discrete-time state-delayed systems [J]. IEEE Transactions on Signal Processing. 2004, 52(6): 1631-1640.
[108] Yue D, Han Q L. Robust H∞filter design of uncertain descriptor systems with discrete and distributed delays [J]. IEEE Transaction on Signal Processing. 2004, 52(11): 3200-3212.
[109] de Souza C E, Trofino A, Barbosa K A. Mode-independent H∞for Markovian jump linear systems [J]. IEEE Transactions on Automatic Control. 2006, 51(11): 1837-1841.
[110] Yang G H, Che W W. Non-fragile H∞filter design for linear continuous-time systems [J]. Automatica. 2008, 44(11): 2849-2856.
[111] Palhares, R M. de Souza C E, Peres P L D. Robust H∞filtering for uncertain discrete-time state-delayed systems [J]. IEEE Transactions on Signal Process. 2001, 49(8): 1696-1703.
[112] Yaz E, Ray A. Linear unbiased state estimation under randomly varying bounded sensor delay [J]. Applied Mathematics Letters. 1998, 11(4): 27-32.
[113] Wang Z, Ho D W C, Liu X. Robust filtering under randomly varying sensor delay with variance constraints [J]. IEEE Transactions on Circuits and Systems II: Express Briefs. 2004, 51(6): 320-326.
[114] Yang F W, Wang Z, Huang Y S, Gani M. H∞control for networked systems with random communication delays [J]. IEEE Transactions on Automatic Control. 2006, 51(3): 511-518.