String Stability of Infinite Interconnected Systems

Zhang Jiye; Yang Yiren; Zeng Jing

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(7): 715-720

Zhang Jiye, Yang Yiren, Zeng Jing. String Stability of Infinite Interconnected Systems[J]. Applied Mathematics and Mechanics, 2000, 21(7): 715-720.

Citation:

Zhang Jiye, Yang Yiren, Zeng Jing. String Stability of Infinite Interconnected Systems[J]. Applied Mathematics and Mechanics, 2000, 21(7): 715-720.

Citation:

Zhang Jiye, Yang Yiren, Zeng Jing. String Stability of Infinite Interconnected Systems[J]. Applied Mathematics and Mechanics, 2000, 21(7): 715-720.

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String Stability of Infinite Interconnected Systems

1.
National Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, P R China;
2.
Institute of Applied Mechanics, Southwest Jiaotong University, Chengdu 610031, P R China

Received Date: 1998-07-24
Rev Recd Date: 2000-04-16
Publish Date: 2000-07-15

Abstract

Abstract

The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced.Intuitively,string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded.Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of inter-connected system are given.The stability regions obtained here are much larger than those in previous papers.The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.
- infinite-dimension,
- interconnected system,
- vector V-function method,
- string stability

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References(13)

References

[1]	Siljak D D. Large-Scale Dynamic Systems Stability and Structure[M]. Amstrerdam: North-Holland,1978.
[2]	Davison E J, Tripathi N. The optimal decentralized control of a large power system: Load and frequence control[J], IEEE Trans Automat Control,1978,23(2):312～325.
[3]	Ei-Sayed M L, Krishnaprasad P S. Homogenous interconnected systems: A example[J]. IEEE Trans Automat Control,1981,26(4):894～901.
[4]	Ozguner U, Barbieri E, Decentralized control of a class of distributed parameter systems[A]. In: Proc IEEE Conf Decision Contr[C]. Dec,1985,932～935.
[5]	Melzer S M, Kuo B C. Optimal regulation of systems described by a countably infinite number of objects[J]. Automatica,1971,7:359～366.
[6]	Levine J, Athans M. On the optimal error regulation of a string of moving vehicles[J]. IEEE Trans Automat Control,1966,11(11):355～361.
[7]	Barbieri E. Stability analysis of a class of interconnected systems[J]. Journal of Dynamic System Measurements Control,1993,115(3):546～551.
[8]	Caudill R E, Garrard W L. Vehicle follower longitudinal control for automated transit vehicles[J]. Journal of Dynamic System Measurements Control,1977,99(4):241～248.
[9]	舒仲周. 比较方程的稳定性[J]. 数学年刊,1986,7(6):676～684.
[10]	舒仲周. 大系统渐近稳定的一般判定定理[J]. 系统科学与数学,1990,10(1):93～96.
[11]	张继业,舒仲周. 大系统渐近稳定的向量V函数法[J]. 控制理论与应用,1996,13(3):386～390.
[12]	Chu K C. Decentralized control of high speed vehicle strings[J]. Transportation Res,1974,362～383.
[13]	Swaroop D, Hedrick J K. String stability of interconnected systems[J]. IEEE Trans Automat Control,1996,41(3):349～357.