ON THE STABILITY OF THE DISCRETE TIME JUMP LINEAR SYSTEM

Adam Czornik, Aleksander Nawrat

2006

Abstract

In this paper we investigate the relationships between individual mode stability and mean square stability of jump linear system. It is well known that generally stability of a dynamical system in all its modes does not guarantee stability of the jump linear system defined by all these modes. We present conditions under which stability of all modes implies the mean square stability of the overall system.

References

  1. K. J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, 1989.
  2. M. Athans, Command and control (C2) theory: A challenge to control science, IEEE Transactions on Automatic Control, vol. 32, 286-293, 1987.
  3. E. K. Boukas and A. Haurie, Manufacturing flow control and predictive maintenance : stochastic control approach, IEEE Transactions on Automatic Control, vol. 35, 1024-1031, 1990.
  4. E. K. Boukas, Q. Zhang and G. Yin, Robust production and maintenance planning in stochastic manufacturing systems, IEEE Transaction on Automatic Control, vol. 40, 1098-1102, 1995.
  5. E. K. Boukas, Z. K. Liu, Production and maintenance control for manufacturing systems, IEEE Transactions on Automatic Control, vol. 46, no. 9, pp. 1455-1460, 2001.
  6. O. L.V. Costa, M. D. Fragoso, Stability results for discretetime linear systems with Markovian jumping parameters, Journal of Mathematical Analysis and Applications, vol. 179, No. 1, pp. 154-178, 1993.
  7. Y. Fang, A. Loparo, Stabilization of continuous-time jump linear systems, IEEE Transactions on Automatic Control, vol. 47, pp. 1596-1603, 2002.
  8. X. Feng, K. A. Loparo, Y. Ji, H. J. Chizeck, Stochastic stability properties of jump linear sytems, IEEE Transactions on Automatic Control, vol. 37, pp. 38-53, 1992.
  9. D. Guo, W. Rugh, A stability result for linear parametervarying systems, Systems and Control Letters, vol. 24, pp. 1-5, 1995.
  10. A. Ilchmann, D. Owens, Pratzel-Wolters, Sufficient conditions for stability of linear time-varying systems, Systems and Control Letters, vol. 9, pp. 157-163, 1987.
  11. Y. Ji, H.J. Chizeck, Controllability, stability, and continuous-time Markovian jump linear quadratic control, IEEE Transactions on Automatic Control, vol. 35, pp. 777-788, 1990.
  12. Y. Ji, H. Chizeck, Optimal quadratic control of jump linear systems with seperately controlled transition probabilities, International Journal of Control, vol 49, no. 2, 481-491, 1989.
  13. Y. Ji, H. Chizeck, Jump linear quadratic Gaussian control: steady-state solution and testable conditions, Control-Theory and Advanced Technology, Vol. 6, No.3, pp.289-319, 1990.
  14. Z. G. Li, Y. C. Soh, C. Y. Wen, Sufficient conditions for almost sure stability of jump linear systems, IEEE Transactions on Automatic Control, vol. 45, no. 7, pp. 1325-1329, 2000.
  15. R. Malhame and C. Y. Chong, Electric load model synthesis by diffusion approximation of a high-order hybridstate stochastic system, IEEE Transactions on Automatic Control, vol. 30, pp. 854-860, 1985.
  16. D. D. Moerder, N. Halyo, J. R. Broussard and A. K. Caglayan, Application of precomputed control laws in a reconfigurable aircraft flight control system, Journal of Guidance, Control and Dynamics, vol. 12, 324- 333,1989
  17. D. B. Petkovski, Multivariable control system design : a case study of robust control of nuclear power plants, Fault Detection and Reliability, vol. 9, 239-246, 1987.
  18. D. D. Siljak, Reliable control using multiple control systems, International Journal on Control, vol. 31, no 2, pp. 303-329, 1980.
  19. D. D. Sworder and R. O. Rogers, An LQ- solution to a control problem associated with solar thermal central receiver, IEEE Transactions on Automatic Control, vol. 28, pp. 971-978, 1983.
  20. D. D. Siljak, Reliable control using multiple control systems, International Journal of Control, vol. 31, no. 2, 303-329, 1980.
  21. A. Swierniak, K. Simek and E. K. Boukas, Intelligent robust control of fault tolerant linear systems, in : H. E. Rauch (ed.), Artificial Intelligence in Real-Time Control, Pergamon, 245-249, 1998.
  22. K. Yasuda, K. Hirai, Upper and lower bounds on the solution of the algebraic Riccati equation, IEEE Transactions on Automatic Control, vol. 24, pp. 483-487, 1979.
  23. H. Weyl, Inequalities between the two kinds of eigenvalues of linear transformation, Proc. Nat. Acad. Sci., vol. 35, pp. 408-411, 1949.
  24. A . Willsky, A survey of design methods for failure detection in dynamics systems, Automatica, vol. 12, 601- 611, 1976.
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Paper Citation


in Harvard Style

Czornik A. and Nawrat A. (2006). ON THE STABILITY OF THE DISCRETE TIME JUMP LINEAR SYSTEM . In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-972-8865-61-0, pages 75-78. DOI: 10.5220/0001202000750078


in Bibtex Style

@conference{icinco06,
author={Adam Czornik and Aleksander Nawrat},
title={ON THE STABILITY OF THE DISCRETE TIME JUMP LINEAR SYSTEM},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2006},
pages={75-78},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001202000750078},
isbn={978-972-8865-61-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - ON THE STABILITY OF THE DISCRETE TIME JUMP LINEAR SYSTEM
SN - 978-972-8865-61-0
AU - Czornik A.
AU - Nawrat A.
PY - 2006
SP - 75
EP - 78
DO - 10.5220/0001202000750078