Positive stabilization of discrete-time systems with unknown delay and bounded controls

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 5616-5622

  Hmamed, Abdelaziz ^a   Benzaouia, Abdellah ^b   Ait Rami, Mustapha ^c   Tadeo, Fernando ^c  

^a SIDI MOHAMED BEN ABDELLAH UNIVERSITY   (Morocco)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

^c UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Bounded controls; Delay systems; Linear programming; Positive systems; Stabilization

Indexed keywords

DIGITAL CONTROL SYSTEMS; LINEAR PROGRAMMING; STABILIZATION; STATE FEEDBACK;

BOUNDED CONTROLS; DELAY SYSTEMS; DISCRETE - TIME SYSTEMS; LINEAR DISCRETE-TIME SYSTEMS; NONNEGATIVE CONTROL; POSITIVE SYSTEMS; STABILIZATION PROBLEMS; STATE FEEDBACK CONTROLLER;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84927720642     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068251     Document Type: Conference Paper

References (24)

1. M. Ait Rami and F. Tadeo, Controller Synthesis for Linear Systems to Impose Positiveness in Closed-Loop States, in 16th IFAC World Congress, Prague, 2005.
2. M. Ait Rami and F. Tadeo, Linear Programming approach to impose positiveness in closed-loop and estimated states, in 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, 2006.
3. M. Ait Rami and F. Tadeo, Positive observation problem for linear discrete positive systems, in Conference on Decision and Control, San Diego, USA, 2006, pp. 4729-4733.
4. M. Ait Rami, F. Tadeo, Controller synthesis for positive linear systems with bounded controls, IEEE Transactions on Circuits and Systems II, vol. 54, no. 2, 2007, pp. 151-155.
5. M. Ait Rami, F. Tadeo and A. Benzaouia, Controller synthesis for discrete positive systems with bounded state and controls, in IEEE American Control Conference, New York, USA, 2007 (submitted).
6. A. Benzaouia and E. Burgat, Regulator problem for linear discretetime systems with non-symmetrical constrained control, International Journal of Control, vol. 48, no. 6, 1988, pp. 2441-2451.
7. F. Blanchini, Set invariance in control, Automatica, vol. 35, no. 11, 1999, pp. 1747-1767.
8. M. Buslowitz and T. Kaczorek, Reachability of positive discrete-time with one time-delay, in National Conf. on Automation of Discrete Processes, Zakopane, 2004 (in Polish).
9. M. Buslowitz and T. Kaczorek, Robust stability of positive discretetime interval systems with time-delays, Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 52, no. 2, 2004, pp. 99-102.
10. M. A. Dahleh and I. J. Diaz-Bobillo, Control of Uncertain Systems: A Linear Programming Approach, Prentice Hall, Englewoods Cliffs, NJ, 1995.
11. L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications, Wiley, New York, 2000.
12. K. Godfrey, Compartmental Models and Their Applications, Academic Press, New York, 1983.
13. W. M. Haddad and V. Chellaboina, Stability Theory for nonnegative and Compartmental Dynamical Systems with Time Delay, Systems & Control Letters, vol. 51, 2004, pp. 355-361.
14. D. Hinrichsen, P. H. A. Ngoc and N. K. Son, Stability radii of positive higher order difference systems, Systems & Control Letters, vol. 49, 2003, pp. 377-388.
15. A. Hmamed, Constrained regulation of linear discrete-time systems with time-delay: delay-dependent and delay independent conditions, International Journal on Systems Science, vol. 31, no. 4, 2000, pp. 529-536.
16. J. A. Jacquez, Compartmental Analysis in Biology and Medicine, 2nd Edition, University of Michigan Press, Ann Arbor, MI, 1985.
17. T. Kaczorek, Positive 1D and 2D Systems. Springer-Verlag, 2002.
18. T. Kaczorek, Stability of positive discrete-time systems with timedelay, in 12th Mediterranean Conf. on Control and Automation, Kasadasi, Turkey, 2004.
19. R. Lewis, and B. D. O. Anderson, Insensitivity of a class of nonlinear compartmental systems to the introduction of arbitrary time delays, IEEE Transactions on Circuits and Systems, vol. 27, 1980, pp. 604-612.
20. Z. Lin and A. Saberi, Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks, Systems and Control Letters, vol. 21, 1995, pp. 225-239.
21. J. M. Maciejowski, Predictive Control with Constraints. Prentice Hall, 2000.
22. Y. Ohta, Qualitative analysis of nonlinear quasi-monotone dynamical systems described by functional-differential equations, IEEE Transactions on Circuits and Systems, vol. 28, 1981, pp. 138-144.
23. A. A. Stoorvogel, A. Saberi and P. Sannuti, Performance with regulation constraints, Automatica, vol. 36, no. 10, 2000, pp. 1443-1456.
24. M. Vassilaki, J. C. Hennet and G. Bitsoris, Feedback control of linear discrete-time systems under state and control constraints, International Journal of Control, vol. 47, no. 6, 1988, pp. 1727-1735.