Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay

Journal of the Franklin Institute

Volumn 336, Issue 8, 1999, Pages 1263-1281

  Cao, Yong Yan ^a   Lam, James ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

DELAY CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; LYAPUNOV METHODS; MARKOV PROCESSES; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; RANDOM PROCESSES; STATE FEEDBACK; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

COUPLED LINEAR MATRIX; DISCRETE TIME LINEAR SYSTEMS; DISTURBANCE ATTENUATION; STATE DELAY SYSTEMS; STOCHASTIC STABILIZABILITY; TIME DELAY;

LINEAR CONTROL SYSTEMS;

EID: 0033307495     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0016-0032(99)00035-6     Document Type: Article

References (30)

1. Krasovskii N.N., Lidskii E.A. Analytical design of controllers in systems with random attributes. Automat. Remote Control, Parts. 1-3(22):1961;1021-1025.
2. Abou-Kandil H., Freiling G., Jank G. Solution and asymptotic behavior of coupled Riccati equations in jump linear systems. IEEE Trans. Automat. Control. 39(8):1994;1631-1635.
3. K. Benjelloun, E.K. Boukas, Independent delay sufficient conditions for robust stability of uncertain linear time-delay systems with jumps, in: Proceedings of the American Control Conference, Albuquerque, New Mexico, June 1997, pp. 3814-3815.
4. Boukas E.K. Control of systems with controlled jump Markov disturbances. Control Theory Adv. Tech. 9(2):1993;577-595.
5. ∞ control for linear systems with Markovian jumping parameters Control Theory Adv. Tech. 9(2):1993;457-466.
6. Feng X., Loparo K.A., Ji Y., Chizeck H.J. Stochastic stability properties of jump linear system. IEEE Trans. Automat. Control. 37:1992;38-53.
7. Ji Y., Chizeck H.J. Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control. 35(7):1990;777-788.
8. H. Kushner, Stochastic Stability and Control, Academic, New York, 1967.
9. M. Mariton. Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990.
10. ∞ control for discrete-time linear systems with Markovian jumping parameters, in: Proceedings of the Thirty Sixth Conference on Decision and Control, San Diego, California, USA, December 1997, pp. 4134-4139.
11. ∞ -control for discrete-time infinite Markov jump parameter systems J. Math. Anal. Appl. 202:1996;578-603.
12. Costa O.L.V., Fragoso M.D. Stability results for discrete-time linear systems with Markovian jumping parameters. J. Math. Anal. Appl. 179:1993;154-178.
13. ∞ control of discrete-time Markovian jump linear systems IEEE Trans. Automat. Control. 43(1):1998;95-100.
14. ∞ control: the discrete-time case, Control Theory Adv. Tech. 10 (4) (1995) 1459-1474.
15. Ji Y., Chizeck H.J. Controllability, observability and discrete-time Markovian jump linear quadratic control. Int. J. Control. 48(2):1988;481-498.
16. Ji Y., Chizeck H.J. Jump linear quadratic Gaussian control: steady-state solution and testable conditions. Control Theory Adv. Tech. 6(3):1990;289-319.
17. Brierley S.D., Chiasson J.N., Lee E.B., Zak S.H. On stability independent of delay for linear systems. IEEE Trans. Automat. Control. 27:1982;252-254.
18. Cheres E., Gutman S., Palmor Z.J. Stabilization of uncertain dynamic systems including state delay. IEEE Trans. Automat. Control. 34:1989;1199-1203.
19. Cao Y.-Y., Sun Y.-X. Robust stabilization of uncertain systems with time-varying multi-state-delay. IEEE Trans. Automat. Control. 43(10):1998;1484-1488.
20. J. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.
21. E.I. Verriest, A.F. Ivanov, Robust stability of delay-difference equations, in: Proceedings of the Thirtyfourth Conference on Decision and Control, New Orleans, LA, December 1995, pp. 386-391.
22. K. Zhou, J.C. Doyle, K. Glover, Robust and Optimal Control, Prentice-Hall, NJ, 1996.
23. ∞ control for uncertain systems with time-varying delays IEE Proc. D: Control Theory Appl. 145(3):1998;338-344.
24. ∞ controller design for linear systems with delayed state and control Automatica. 31:1995;917-919.
25. ∞ controllers for state delayed systems IEEE Trans. Automat. Control. 39:1994;159-161.
26. ∞ -control of discrete-time linear systems with nome-bounded uncertainties and time delay in state Automatica. 34(1):1998;137-139.
27. Morozan T. Stochastic stability and control for discrete-time systems with jump Markov disturbances. Rev. Roum. Math. Pures Appl. Tome XXIV(1):1979;111-127.
28. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
29. Rami M.A., Ghaoui L.E. LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE Trans. Automat. Control. 41(11):1996;1666-1671.
30. Mariton M., Bertrand P. A homotopy algorithm for solving coupled Riccati equations. Opt. Control Appl. Methods. 6:1984;351-357.