Delay-dependent robust stability and H∞ control of jump linear systems with time-delay

International Journal of Control

Volumn 74, Issue 4, 2001, Pages 329-340

  Boukas, E K ^a   Liu, Z K ^a   Liu, G X ^a  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DELAY CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; GAIN CONTROL; MATRIX ALGEBRA; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); STATE FEEDBACK; SYSTEM STABILITY; UNCERTAIN SYSTEMS;

POLYTOPIC UNCERTAIN PARAMETERS;

LINEAR CONTROL SYSTEMS;

EID: 0035836301     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207170010008752     Document Type: Article

References (26)

1. Benjelloun, K., and Boukas, E.K., 1998, Mean square stochastic stability of linear time-delay system with Markovian jumping parameters. IEEE Transactions on Automatic Control, 43.
2. Benjelloun, K., Boukas, E.K., and Yang, H., 1996, Robust stabilizability of uncertain linear time-delay systems with Markovian jumping parameters. Journal of Dynamic Systems Measurements, 118.
3. Boukas, E.K., 1993, Control of system with controlled jump Markov disturbances. Control Theory and Advanced Techonology, 9, 577-597.
4. Boukas, E.K., and Yang, H., 1998, Robust stability of linear piecewise deterministic systems under matching conditions. Control-theory and Advanced Technology, 10, 1541-1549.
5. ∞ control of discrete-time jump linear systems with time-delay: an LMI approach. Submitted for publication.
6. Boukas, E.K., and Liu, Z.K., 2000, Jump linear quadratic regulator with controlled jump rate. IEEE Transaction on Automtic Control, 45.
7. Boukas, E.K., and Yang, H., 1995, Stability of discrete-time linear systems with Markovian jumping parameters. Mathematics of Control, Signals and Systems, 8, 390-402.
8. Boyd, S., Ghaoui, El.L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory (SIAM).
9. ∞ control for uncertain systems with time-varying delays. IEE Proceedings-Control Theory and Applications, 145, 338-344.
10. Costa, O.L., and Boukas, E.K., 1998, Necessary and sufficient condition for robust stability and stabilizability of continuous time linear systems with Markovian jumps. Journal of Optimization Theory and Applications, 99.
11. Costa, O.L.V., and Fragoso, M.D., 1993, Stability results for discrete-time Markovian jump linear systems with Markovian jumping parameters systems. Journal of Mathematical Analysis and Applications, 179, 154-178.
12. Davis, M.H.A., 1993, Markov Modeling and Optimization (Chapman and Hall).
13. Feng, X., Loparo, K.A., Ji, Y., and Chizeck, H.J. 1992, Stochastic stability properties of jump linear systems. IEEE Transaction on Automatic Control, 37, 38-53.
14. ∞ output feedback controller design for linear systems with time-varying delayed state. IEEE Transactions on Automatic Control, 43, 971-974.
15. Ji, Y., and Chizeck, H.J., 1990, Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 35, 777-788.
16. Gahinet, P., Nemirovski, A., Laub, A.J., and Chilai, M., 1995, LMI Control Toolbox: For use with Matlab, The Math Works Inc.
17. Liu, G.X., and Hou, Z.T., 1998, Piecewise deterministic processes and Markov modelling for non-diffusion stochastic systems with continuous parameter. Proceedings of 2nd International Symposium on Semi-Markov Models: Theory and Applications, France.
18. Mariton, M., 1990, Jump Linear Systems in Automatic Control (New York: Marcel Dekker).
19. Mahmoud, M.S., and Al-Muthairi, N.F., 1994, Design of robust controllers for time-delay systems. IEEE Transactions on Automatic Control, 39, 995-999.
20. Niculescu, S.I. Nero, A.T., Dion, J.M., and Dugard, L., 1995, Delay-dependant stability of linear systems with delayed state: An LMI approach. Proceeding of 34th IEEE CDC, Vol. 2, pp 1495-1496, New Orleans, LA, USA, pp. 1495-1496.
21. Park, P., 1999, A delay-dependant stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control, 44.
22. Petersen, I.R., 1987, A stabilization algorithm for a class of uncertain linear systems. System and Control Letter, 351-357.
23. ∞ Control for Markovian jumping liners systems with parametric uncertainty. Journal of Optimization Theory and Applications, 95.
24. ∞ control for linear systems with Markovian jumping parameters. Control-Theory and Advanced Technology, 9, 457-466.
25. Sworder, D.D., and Robinson, V.G., 1974, Feedback regulators for jump parameters systems with state and control dependant transitions rates. IEEE Transactions on Automatic Control, 18, 355-359.
26. Wonham, W.M., 1971, Random differential equations in control theory. In A.T. Bharucha-ried (Ed) Probabilistic Methods in Applied Mathematics, Vol. 2 (New York: Academic Press).