JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (11): 91-97.doi: 10.6040/j.issn.1671-9352.0.2015.167

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Stabilization for discrete-time systems with multiple input delays

LI Lin, ZHANG Huan-shui   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China
  • Received:2015-04-16 Revised:2015-07-22 Online:2015-11-20 Published:2015-12-09

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Abstract: Under some constraint on the system matrix and input matrix, the necessary and sufficient stabilization condition and the stabilizing controller for the system were proposed. Our approach is to convert the original problem into an equivalent stabilization problem for delay-free system on the basis of system reduction.

Key words: input delay, system reduction, stabilization

CLC Number: 

  • TP13
[1] KOLMANOVSKII V B, MYSHKIS A. Introduction to the theory and applications of functional differential equations[M]. Dordrecht:Kluwer Academy, 1999.
[2] ROSS D W, FlVGGE-LOTZ I. An optimal control problem for systems with differential-difference equation dynamics[J]. SIAM Journal on Control, 1969, 7(4):609-623.
[3] KOIVO H N, LEE E B. Controller synthesis for linear systems with retarded state and control variables and quadratic cost[J]. Automatica, 1972, 8(2):203-208.
[4] ZHANG Huanshui, DUAN Guangren, XIE Lihua. Linear quadratic regulation for linear time-varying systems with multiple input delays[J]. Automatica, 2006, 42(9):1465-1476.
[5] LIU Chongyang, LOXTON R, TEO K L. A computational method for solving time-delay optimal control problems with free terminal time[J]. Systems & Control Letters, 2014, 72:53-60.
[6] CHOI H H, CHUNG M J. Memoryless H∞ controller design for linear systems with delayed state and control[J]. Automatica, 1995, 31(6):917-919.
[7] TADMOR G. The standard H∞ problem in systems with a single input delay[J]. IEEE Transactions on Automatic Control, 2000, 45(3):382-397.
[8] TADMOR G, MIRKIN L. H∞ control and estimation with preview-part II:fixed-size ARE solutions in discrete time[J]. IEEE Transactions on Automatic Control, 2005, 50(1):29-40.
[9] KRASOVSKII N N. Stability of motion[M]. Stanford CA:Stanford University Press, 1963.
[10] GU Keqin. Discretization schemes for Lyapunov-Krasovskii functionals in time delay systems[J]. Kybernetica, 2001, 37(4):479-504.
[11] NICULESCU S I. Delay effects on stability:a robust control approach[M]. Berlin:Springer, 2001.
[12] ZHAO Xudong, ZHANG Lixian, SHI Peng. Stability of a class of switched positive linear time-delay systems[J]. International Journal of Robust and Nonlinear Control, 2013, 23(5):578-589.
[13] OLBROT A W. Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays[J]. IEEE Transactions on Automatic Control, 1978, AC-23(5):887-890.
[14] WATANABE K, ITO M. A process-mode control for linear systems with delay[J]. IEEE Transactions on Automatic Control, 1981, AC-26(6):1261-1269.
[15] KWON W H, PEARSON A E. Feedback stabilization of linear systems with delayed control[J]. IEEE Transactions on Automatic Control, 1980, AC-25(2):266-269.
[16] ARTSTEIN Z. Linear systems with delayed controls:a reduction[J]. IEEE Transactions on Automatic Control, 1982, AC-27(4):869-879.
[17] ZHOU Bin. Stabilization of discrete-time systems with multiple actuator delays and saturations[J]. IEEE Transactions on Circuits and SystemsⅠ:Regular Papers, 2013, 60(2):389-400.
[18] JI Kun. Real-time control over networks[D]. Texas:A & M University, 2006.
[19] IONETE C, CELA A, GAID M B. Controllability and observability of input/output delayed discrete systems[C]//Proceedings of the 2006 American Control Conference, 2006:3513-3518.
[20] HAUTUS M L J. Stabilization controllability and observability of linear autonomous systems[C]//Indagationes Mathematicae, 1970, 32:448-455.
[21] 郑大钟.线性系统理论[M].2版.北京:清华大学出版社,2002. ZHENG Dazhong. Linear system theory[M]. 2nd ed. Beijing:Press of Tsinghua University, 2002.
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