STRING STABILITY OF INFINITE INTERCONNECTED SYSTEMS

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 interconnected 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.

2010 MSC Number:

O317
TP13

Zhang Jiye;Yang Yiren;Zeng Jing . STRING STABILITY OF INFINITE INTERCONNECTED SYSTEMS. Applied Mathematics and Mechanics (English Edition), 2000, 21(7): 791-796.

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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] Shu Zhongzhou.The stability of the comparison equations[J].Chinese Annals of Mathematics,1986,7(6):676~684.(in Chinese)
[10] Shu Zongzhou.General theorems on the asymptotically stability of large scale systems[J].System Science and Mathematical Sciences,1990,10(1):93~96.(in Chinese)
[11] Zhang Jiye,Shu Zhongzhou.The vector V-functions method of the asymptotic stability for the large-scale systems[J].Control Theory and Applications,1996,13(3):386~390.(in Chinese)
[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.

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