Guaranteed Cost Control for Uncertain Markovian Jump Systems with Mode-Dependent Time-Delays

IEEE Transactions on Automatic Control

Volumn 48, Issue 12, 2003, Pages 2270-2277

  Chen, Wu Hua ^a   Xu, Jian Xin ^b   Guan, Zhi Hong ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Guaranteed cost control; Jump linear systems; Linear matrix inequality (LMI); Norm bounded uncertainty; Time delay systems

Indexed keywords

GUARANTEED COST CONTROL; NORM-BOUNDED UNCERTAINTY; TIME-DELAY SYSTEMS;

CLOSED LOOP CONTROL SYSTEMS; CONTROL EQUIPMENT; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; LYAPUNOV METHODS; MARKOV PROCESSES; STABILIZATION; STATE FEEDBACK; VECTORS;

UNCERTAIN SYSTEMS;

EID: 0347316618     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.820165     Document Type: Article

References (25)

1. O. L. V. Costa and M. D. Fragoso, "Stability results for discrete-time systems with Markovian jumping parameters," J. Math. Anal. Applicat., vol. 179, pp. 154-178, 1993.
2. Y. Ji and H. J. Chizeck, "Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control," IEEE Trans. Automat. Contr., vol. 35, pp. 777-788, July 1990.
3. ∞ control for Markovian jumping linear systems with parametric uncertainty," J. Optim. Theory Applicat., vol. 95, no. 1, pp. 75-99, 1997.
4. ∞ control of uncertain Markovian jump systems with time-delay," IEEE Trans. Automat. Contr., vol. 45, pp. 77-83, Jan. 2000.
5. ∞, control of jump linear systems with time delay," Int. J. Control, vol. 74, no. 4, pp. 329-340, 2001.
6. E. K. Boukas and Z. K. Liu, "Robust stability and stabilizability of jump linear uncertain system with mode-dependent time-delays," in, Proc. Amer. Control Conf., Arlington, VA, 2001, pp. 884-889.
7. ∞, control of discrete-time Markovian jump linear systems with mode-dependent time-delays," IEEE Trans. Automat. Contr., vol. 46, pp. 1918-1924, Dec. 2001.
8. _, "Output feedback guaranteed cost control for uncertain time-delay systems with Markov jumps," in Proc. Amer. Control Conf., Chicago, IL, 2000, pp. 2784-2788.
9. E. K. Boukas and P. Shi, "Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters," Int. J. Robust Nonlinear Control, vol. 8, no. 13, pp. 1155-1167, 1998.
10. X. Li and C. E. de Souza, "Delay-dependent robust stability and stabilization of uncertain linear delay system: a linear matrix inequality approach," IEEE Trans. Automat. Contr., vol. 42, pp. 1144-1148, Aug. 1997.
11. ∞, control of distributed delay syatems with application to combustion control," IEEE Trans. Automat. Contr., vol. 46, pp. 1930-1935, Oct. 2001.
12. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, "Delay-dependent robust stabilization of uncertain state-delayed systems," Int. J. Control, vol. 74, no. 14, pp. 1447-1455, 2001.
13. ∞ control of linear time-delay systems," IEEE Trans. Automat. Contr., vol. 47, pp. 253-270, Feb. 2002.
14. E. Fridman, "New lyapunov-krasovskii functionals for stability of linear retard and neutral type systems," Syst. Control. Lett., vol. 43, pp. 309-319, 2001.
15. S. Phoojaruenchanachai and K. Furuta, "Memoryless stabilization of uncertain linear systems including time-varying state delays," IEEE Trans. Automat. Contr., vol. 37, pp. 1022-1026, July 1992.
16. M. S. Mahmoud and N. F. Al-Muthairi, "Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties," IEEE Trans. Automat. Contr., vol. 39, pp. 2135-2139, Oct. 1994.
17. Y. Wang, L. Xie, and C. E. de Souza, "Robust control of a class of uncertain nonlinear system," Syst. Control Lett., vol. 19, pp. 139-149, 1992.
18. Y. S. Lee, Y. S. Moon, and W. H. Kwon, "Delay-dependent guaranteed cost control for uncertain state-delayed systems," in Proc. Amer. Control Conf., Arlington, VA, 2001, pp. 3376-3381.
19. S. O. R. Moheimani and I. R. Peterson, "Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems," IEE Proc. Control Theory Applicat., vol. 144, no. 2, pp. 183-188, 1997.
20. S. H. Esfahani and S. O. R. Moheimani, "LMI approach to guaranteed cost control of linear uncertain time-delay system," IEE Proc. Control Theory Applicat., vol. 145, no. 6, pp. 491-498, 1998.
21. L. Yu and J. Chu, "An LMI appoach to guaranteed cost control of linear uncertain time-delay system," Automatica, vol. 35, pp. 1155-1159, 1999.
22. K. Yamanaka, K. Uchida, and E. Shimemura, "Optimal control of systems with random delay," Int. J. Control, vol. 29, no. 3, pp. 489-495, 1979.
23. I. Kolmanovsky and T. L. Maizenberger, "Stochastic stability of nonlinear systems with randomly varying time-delay," in Proc. Amer. Control Conf., Chicago, IL, 2000, pp. 4304-4308.
24. I. Kolmanovsky and T. Maizenberg, "Optimal control of continuous-time linear systems with a time-varying random delay," Syst. Control Lett., vol. 44, pp. 119-126, 2001.
25. ∞ control for uncertain stochastic systems with state delay," IEEE Trans. Automat. Contr., vol. 47, pp. 2089-2094, Dec. 2002.