H∞ control and estimation of retarded state-multiplicative stochastic systems

IEEE Transactions on Automatic Control

Volumn 52, Issue 9, 2007, Pages 1773-1779

  Gershon, E ^a   Shaked, U ^b   Berman, N ^c  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Stochastic H control; Time delay systems; Uncertain systems

Indexed keywords

CONTINUOUS TIME SYSTEMS; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; PARAMETER ESTIMATION; TIME DELAY; UNCERTAIN SYSTEMS;

INPUT-OUTPUT APPROACH; STATE-MULTIPLICATIVE STOCHASTIC SYSTEM;

STOCHASTIC CONTROL SYSTEMS;

EID: 34648840397     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.904618     Document Type: Article

References (29)

1. Y.-P. Huang and K. Zhou, "Robust stability of uncertain time-delay systems," IEEE Trans. Autom. Control, vol. 45, pp. 2169-2173, 2000.
2. C.-Y. Kao and B. Lincoln, "Simple stability criteria for systems with time-varying delays," Automatica, vol. 40, pp. 1429-1434, 2004.
3. E. Gershon, U. Shaked, and I. Yaesh, "H∞ control and estimation of state-multiplicative linear systems," in Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer, 2005, vol. 318.
4. O. L. V. Costa and C. S. Kubrusly, "State-feedback H∞-control for discrete-time infinite-dimensional stochastic bilinear systems," J. Math. Syst., Estim. Contr., vol. 6, pp. 1-32, 1996.
5. V. Dragan and T. Morozan, "Mixed input-output optimization for time-varying Ito systems with state dependent noise," Dyn. Continuous, Discrete Impulsive Syst., vol. 3, pp. 317-333, 1997.
6. V. Dragan, T. Morozan, and A. Halanay, "Optimal stability compensator for linear systems with state dependent noise," Stochastic Anal. Applicat., vol. 10, pp. 557-572, 1992.
7. D. Hinrichsen and A. J. Pritchard, "Stochasic H∞," SIAM J. Contr. Optim., vol. 36, no. 5, pp. 1504-1538, 1998.
8. V. A. Ugrinovsky, "Robust H∞ control in the presence of stochastic uncertainty," Int. J. Contr., vol. 71, pp. 219-237, 1989.
9. E. Gershon, D. J. N. Limebeer, U. Shaked, and I. Yaesh, "Robust H & filtering of stationary continuous-time linear systems with stochastic uncertainties," IEEE Trans. Autom. Control, vol. 46, no. 11, pp. 1788-1793, 2001.
10. V. Dragan and A. Stoica, "A γ attenuation problem for discrete-time time-varying stochastic systems with multiplicative noise," Inst. Math. Romanian Acad., no. 10, 1998.
11. A. El Bouhtouri, D. Hinrichsen, and A. J. Pritchard, H∞-type control for discrete-time stochasic systems," Int. J. Robust Nonlinear Contr., vol. 9, pp. 923-948, 1999.
12. E. Gershon, U. Shaked, and I. Yaesh, "Robust H∞ Estimation of stationary discrete-time linear processes with stochastic uncertainties," Syst. Contr. Lett., vol. 45, pp. 257-269, 2002.
13. V. Kolmanovskii and J.-P. Richard, "Stability of some linear systems with delays," IEEE Trans. Autom. Control, vol. 44, pp. 984-989, 1999.
14. X. Li and C. de Souza, "Criteria for robust stability and stabilization of uncertain linear systems with state delay," Automatica, vol. 33, pp. 1657-1662, 1997.
15. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, "Delay-dependent robust stabilization of uncertain state-delayed systems," Int. J. Contr. vol. 74, pp. 1447-1455, 2001.
16. S. I. Niculescu, Delay Effects On Stability: A Robust Control Approach, Lecture Notes in Control and Information Sciences. London, U.K.: Springer-Verlag, 2001, vol. 269.
17. E. Fridman, "New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems," Syst. Contr. Lett., vol. 43, pp. 309-319, 2001.
18. X. Mao, "Robustness of exponential stability of stochastic differential delay equations," IEEE Trans. Autom. Control, vol. 41, pp. 442-447, 1996.
19. J. Yong and X. Y. Zhou, "Stochastic Controls: Hamiltonian Systems and HJB equations," in Applications of Mathematics: Stochastic Modelling and Applied Probability. Berlin, Germany: Springer, 1999, vol. 43.
20. D. Yue and S. Won, "Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties," Electron. Lett., vol. 37, pp. 992-993, 2001.
21. S. Xu and T. Chen, "Robust H∞ control for uncertain stochastic systems with state-delay," IEEE Trans. Autom. Control, vol. 47, pp. 2089-2094, 2002.
22. S. Xu, J. Lam, X. Mao, and Y. Zou, "A new LMI condition for delay-dependent robust stability of stochastic time-delay systems," Asian J. Contr., vol. 7, pp. 419-423, 2005.
23. W.-H. Chen, Z.-H. Guan, and X. Lu, "Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: An LMI approach," Syst. Contr. Lett., vol. 54, pp. 547-555, 2005.
24. E.-K. Boukas and Z.-K. Liu, Deterministic and Stochastic Time Delay Systems. Berlin, Germany: Birkhauser, 2002.
25. X. Mao and A. Shah, "Exponential stability of stochastic delay differential equations," Stochastics Stochastics Rep., vol. 60, no. 1, pp. 135-153, 1997.
26. E. I. Varriest and P. Florchinger, "Stability of stochastic systems with uncertain time delays," Syst. Contr. Lett., vol. 24, no. 1, pp. 41-47, 1995.
27. P. Florchinger and E. I. Varriest, "Stabilization of nonlinear stochastic systems with Dekay feedback," in Proc. 32nd IEEE Conf. Decision Contr., San Antonio, TX, Dec. 1993, pp. 859-860.
28. E. I. Varriest, S.-I. Niculesescu and K. Gu, Eds., "Asymptotic properties of stochastic delay systems," in Advances in Time-Delay Systems. Berlin, Germany: Springer-Verlag, 2004, pp. 389-435.
29. E. Fridman and U. Shaked, "Input-output approach to stability and L 2 - gain analysis of systems with time-varying delays," Syst. Contr. Lett., vol. 55, pp. 1041-1053, 2006.