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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 490903, 11 pages
http://dx.doi.org/10.1155/2012/490903
Research Article

Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

1Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
2State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
3School of Electrical and Electronics Engineering, East China Jiaotong University, Nanchang 330013, China
4School of Electric and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China
5Guangxi Key Laboratory of Automobile Components and Vehicle Technology, Liuzhou 545006, China

Received 27 August 2012; Accepted 10 October 2012

Academic Editor: Valery Y. Glizer

Copyright © 2012 Hong Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. E. Kalman, “On the general theory of control systems,” in Proceedings of the 1st International Conference on Automatic Control, vol. 1, pp. 481–492, Moscow, Russia, 1960.
  2. R. E. Kalman, Y. C. Ho, and K. S. Narendra, “Controllability of linear dynamical systems,” vol. 1, pp. 189–213, 1963. View at Zentralblatt MATH
  3. D. H. Chyung, “On the controllability of linear systems with delay in control,” IEEE Transactions on Automatic Control, vol. 15, no. 2, pp. 255–257, 1970.
  4. D. H. Chyung, “Controllability of linear systems with multiple delays in control,” IEEE Transactions on Automatic Control, vol. 15, no. 6, pp. 694–695, 1970. View at Publisher · View at Google Scholar
  5. K. Watanabe, “Further study of spectral controllability of systems with multiple commensurate delays in state variables,” International Journal of Control, vol. 39, no. 3, pp. 497–505, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. V. N. Phat, “Controllability of discrete-time systems with multiple delays on controls and states,” International Journal of Control, vol. 49, no. 5, pp. 1645–1654, 1989. View at Publisher · View at Google Scholar
  7. V. N. Phat and T. C. Dieu, “Constrained controllability of linear discrete nonstationary systems in Banach spaces,” SIAM Journal on Control and Optimization, vol. 30, no. 6, pp. 1311–1318, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. V. Savkin and I. R. Petersen, “Weak robust controllability and observability of uncertain linear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 1037–1041, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. V. Y. Glizer, “Euclidean space controllability of singularly perturbed linear systems with state delay,” Systems & Control Letters, vol. 43, no. 3, pp. 181–191, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. C. J. Wang and H. E. Liao, “Impulse observability and impulse controllability of linear time-varying singular systems,” Automatica, vol. 37, no. 11, pp. 1867–1872, 2001.
  11. P. Chen and H. Qin, “Controllability of linear systems in Banach spaces,” Systems & Control Letters, vol. 45, no. 2, pp. 155–161, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1980.
  13. E. D. Sontag, Mathematical Control Theory: Deterministic Finite-Dimensional Systems, vol. 6, Springer, New York, NY, USA, 1990. View at Publisher · View at Google Scholar