Control of singularly perturbed systems with Markovian jump parameters: an H∞ approach

Automatica

Volumn 35, Issue 8, 1999, Pages 1369-1378

  Drǎgan, Vasile ^a   Peng, Shi ^b   Boukas, El Kébir ^c  

^a INSTITUTE OF MATHEMATICS   (Romania)

^b UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

^c GERAD   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; RICCATI EQUATIONS; STATE SPACE METHODS; SYSTEM STABILITY;

LINEAR CONTINUOUS TIME SYSTEMS; MARKOVIAN JUMP PARAMETERS; STOCHASTIC STABILITY;

OPTIMAL CONTROL SYSTEMS;

EID: 0033177763     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(99)00047-3     Document Type: Article

References (26)

1. Boukas, E. K., & Haurie, A. (1990). Manufacturing flow control and preventive maintenance: A stochastic control approach. IEEE Transactions on Automatic Control, 35(7), 1024-1031.
2. Boukas, E. K., Zhang, Q., & Yin, G. (1995). Robust production and maintenance planning in stochastic manufacturing systems. IEEE Transactions on Automatic Control, 40(6), 1098-1102.
3. Boukas, E. K., Zhu, Q., & Zhang, Q. (1994). Piecewise deterministic Markov process model for flexible manufacturing systems with preventive maintenance, Journal of Optimization Theory and Applications, 81(2), 259-275.
4. Chizeck, H. J., Willsky, A. S., & Castanon, D. (1986). Discrete-time Markovian-jump linear quadratic optimal control, International Journal of Control, 43(1), 213- 231.
5. ∞ filtering for Markovian jump linear systems. In Proceedings of 35th IEEE Conference on Decision and Control Kobe, Japan (pp. 4814-4818).
6. ∞ control for linear systems with Markovian jumping parameters. Control-theory and Advanced Technology, 9(1), 457-466.
7. Dragan, V. (1993). Asymptotic expansions for game-theoreic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems. System and Control Letters, 20(6), 455-463.
8. ∞-norms and disturbance attenuation for systems with fast transients. IEEE Transactions on Automatic Control, 41(5), 747-750.
9. Feng, X., & Loparo, K. A. (1990). Almost sure instability of the random harmonic oscillator, SIAM Journal of Applied Mathematics, 50(3), 744-759.
10. Fragoso, M. D. (1988). On a partially observable LQG problem for systems with Markovian jumping parameters and quadratic cost. System and Control Letters, 10(5), 349-356.
11. Gaitsgory, V. (1993). Suboptimal control of singularly perturbed systems and periodic optimization. IEEE Transactions on Automatic Control, 38(6), 888-903.
12. Ji, Y., & Chizeck, H. J. (1990). Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 35(1), 777-788.
13. Krasovskii, N. N., & Lidskii, E. A. (1961). Analysis design of controller in systems with random attributes - Part 1. Automatic Remote Control, 22, 1021-1025.
14. Mariton, M., & Bertrand, P. (1985). Output feedback for a class of linear systems with stochastic jump parameters. IEEE Transactions on Automatic Control, 30(9), 898-900.
15. Morozan, T. (1983). Optimal stationarycontrol for dynamic systems with markov perturbations. Stochastic Analysis and Applications 1(3), 299-325.
16. Morozan, T. (1996). Parametrized Riccatiequations for Controlled Linear Differential Systems with Jump Markovperturbations. Technical Report, Institute of Math. of Romanian Academy, 20/1996.
17. ∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements. Automatica, 29(2), 401-423.
18. ∞-optimal control for singularly perturbed systems. Part II: Imperfect state measurements. IEEE Transactions on Automatic Control, 39(2), 280-299.
19. ∞-control of jump linear systems. In Proceedings of Sixth International Symposium on Dynamic Games and Applications St-Jovite, Quebec, Canada (pp. 466-474).
20. ∞ control of large scale jump linear systems via averaging and aggregation. In Proceedings of 34th IEEE Conference on Decision and Control, New Orleans, LA (pp. 2574-2579).
21. Pan, Z., & Basar, T. (1995b). Multi-time scale zero-sum differential games with perfect state measurements. Dynamics and Control, 5(5), 7-29.
22. Pan, Z., & Basar, T. (1996). Random evolutionary time-scale decomposition in robust control of jump linear systems. In Proceedings of 35th IEEE Conference on Decision & Control, Kobe, Japan. (pp. 505-510).
23. Shi, P. (1996). Robust control for linear systems with Markovian jumping parameters. In Preprints of 13th IFAC World Congress, San Francisco, USA (pp. 433-438).
24. ∞ control for Markovian jumping linear systems with parametric uncertainty, Journal of Optimization Theory and Applications, 95(1), 75-99.
25. Sworder, D. D. (1969). Feedback control of a class of linear systems with jump parameters, IEEE Transactions on Automatic Control, 14(1), 9-14.
26. Wonham, W. M. (1971). Random differential equations in control theory. In A. T. Bharucha-reid, In Probabilistic Methods in Applied Mathematics, Academic Press, New York. (pp. 131-213).