Design of robust controller for linear systems with Markovian jumping parameters

Mathematical Problems in Engineering

Volumn 4, Issue 4, 1998, Pages 269-288

  Benjelloun, K ^a   Boukas, E K ^a   Costa, O L V ^b   Shi, P ^c  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Linear systems with Markovian jumping parameters; Markov process; Norm bounded uncertainties; Stochastic stability

Indexed keywords

EID: 0001411622     PISSN: 1024123X     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1024123X98000830     Document Type: Article

References (29)

1. Abou-Kandil, H., Freiling, G. and Jank, G., Solution and asymptotic behavior of coupled Riccati equations in jump linear systems, IEEE Transactions on Automatic Control, 39(8), 1631-1636, 1994.
2. Boukas, E.K. and Haurie, A., Manufacturing flow control and preventive maintenance: a stochastic control approach, IEEE Transactions on Automatic, AC-35(9), 1024-1031, 1990.
3. Boukas, E.K. and Mignanego, F., On the stochastic controllability of linear piecewise deterministic systems,. Working report, 1992.
4. Boukas, E.K., Control of systems with controlled jump Markov disturbances, Control Theory and Advanced Technology, 9(2), 577-595, 1993.
5. Boukas, E.K., Robust stabilizability of linear piecewise deterministic systems under matching conditions, Control Theory and Advanced Technology, 9(2), 577-595, 1993.
6. Boukas, E.K. and Yang, H., Robust stabilizability of nonlinear piecewise deterministic systems under matching conditions, Mathematical Problems in Engineering: Theory, Methods and Applications, 1997.
7. Boukas, E.K., Zhu, Q. and Zhang, Q., A piecewise deterministic Markov process model for flexible manufacturing systems with preventive maintenance, Journal of Optimization Theory and Applications, 81(2), 259-275, 1994.
8. Costa, O.L.V., Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of Mathematical Analysis and Applications, 179, 154-178, 1993.
9. Costa, O.L.V., Linear minimum mean square error estimation for discrete-time Markovian jump linear systems, IEEE Transactions on Automatic Control, 39(8), 1685-1688, 1994.
10. Costa, O.L.V., Mean-square stabilizing solutions for discrete-time coupled algebraic Riccati equations, IEEE Transactions on Automatic Control, 41(4), 593-598, 1996.
11. Davis, M.H.A., Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models, J. Roy. Stabit. Soc. B, 46, 353, 1984.
12. ∞ control for linear systems with Markovian jumping parameters, Control Theory and Advanced Technolgy, 9(2), 457-466, 1993.
13. Doob, J.L., Stochastic Processes, John Wiley & Sons, 1990.
14. Doyle, J.C., Francis, B.A. and Tannenbaum, A.R., Feeback Control Theory, Macmillan Publishing Company, New York, 1992.
15. Feng, X., Loparo, A., Ji, Y. and Chizeck, H.J. Stochastic stability properties of jump linear systems, IEEE, Trans on Automatic Control, 37(1), 38-53, 1992.
16. Hopkins, W.E., Comments on Robust jump linear quadratic control: A mode stabilizing solution, IEEE Trans. on Automatic Control, AC-31(11), 1079-1081, 1986.
17. Ji, Y. and Chizeck, H., Controllability, stability, and continuous-time Markovian jump linear quadratic control, IEEE Transactions on Automations Control, 35(7), 777-788, 1990.
18. Krasovskii, N.M. and Lidskii, E.A., Analytical design of controllers in systems with random attributes I-II-III, Automation Remote Control, 22, 1021,1141,1289,1961.
19. Kats, I. and Krasovskii, N.M., On the stability of systems with random parameters, P.M.M., 24(5), 809, 1960.
20. Leondes, C.T., Robust control system techniques and applications, Part 1 and Part 2, Control Dynamics Systems, 50, 119-174, 1992.
21. Lunze, J., Robust Multivariable Control, Prentice Hall International, New York, 1988.
22. Petersen, I.R. and Hollot, C.V., A Riccati equations approach to the stabilization of uncertain linear systems, Automatica, 22, 397-411, 1986.
23. Petersen, I.R., Some new results on algebraic Riccati equations in linear quadratic differential games and stabilization on uncertain linear systems, Systems Control Letters, 10, 341-348, 1988.
24. Mariton, M. and Bertrand, P., Robust jump linear quadratic control: A mode stabilizing solution, IEEE Transactions on Automatic Control, AC-30, 1145, 1985.
25. Mariton, M., Jump Linear Systems in Automatic Control, New York and Basel, 1990.
26. Rishel, R., Control of system with jump Markov disturbances, IEEE Transactions on Automatic Control, AC-20, 241, 1975.
27. Sworder, D., Feedback control of a class of linear systems with jump parameters, IEEE Transactions on Automatic Control, AC-14, 9, 1969.
28. Vermes, D., Optimal control of piecewise deterministic Markov process, Stochastics, 14, 165, 1985.
29. Wonham, W.M., Random differential equations in control theory, Probabilistic Methods in Applied Mathematics, Vol. 2, A.T. Beruche-reid, Ed., N.Y., 1971.