H∞-type control for discrete-time stochastic systems

International Journal of Robust and Nonlinear Control

Volumn 9, Issue 13, 1999, Pages 923-948

  El Bouhtouri, A ^a   Hinrichsen, D ^b   Pritchard, A J ^c  

^a FACULTÉ DES SCIENCES   (Morocco)

^b UNIVERSITY OF BREMEN   (Germany)

^c UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONTROL SYSTEM ANALYSIS; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; PERTURBATION TECHNIQUES; SYSTEM STABILITY;

LINEAR MATRIX INEQUALITIES (LMI); NONLINEAR MATRIX INEQUALITIES;

STOCHASTIC CONTROL SYSTEMS;

EID: 0033339993     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199911)9:13<923::AID-RNC444>3.0.CO;2-2     Document Type: Article

References (26)

1. ∞,, SIAM J. Control Optim., 36, 1504-1538 (1998).
2. Arnold, L., Stochastic Differential Equations: Theory and Applications, Wiley, New York, 1974.
3. Ibrahim, R. A., Parametric Random Vibration, Research Studies Press, Letchworth, England, 1985.
4. Kubrusly, C. S., 'On discrete stochastic bilinear systems stability', J. Math. Anal. Appl., 113, 36-58 (1986).
5. Wonham, W. M., 'Optimal stationary control of a linear system with state dependent noise', SIAM J. Control Optim., 5, 486-500 (1967).
6. Hausmann, U. G., 'Optimal stationary control with state and control dependent noise', SIAM J. Control Optim., 9, 184-198 (1971).
7. Kushner, H., Stochastic Stability and Control, Academic Press, New York, 1967.
8. Kozin, J., 'A survey of stability of stochastic systems', Automatica, 5, 95-112 (1969).
9. Curtain, R. F. (Ed.), Stability of Stochastic Dynamical Systems, Lecture Notes in Mathematics, Vol. 294, Springer, Berlin, 1972.
10. ∞ Control Problem: A State Space Approach, Prentice-Hall, New York, 1992.
11. Green, M. and D. J. N. Limebeer, Linear Robust Control, Prentice-Hall, Englewood Cliffs, NJ, 1995.
12. Zhou, K., J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice-Hall, New Jersey, 1996.
13. El Bouhtouri, A. and A. J. Pritchard, 'A Riccati equation approach to maximizing the stability radius of a linear system by state feedback under structured stochastic Lipschitzian perturbations', Systems Control Lett., 21, 475-484 (1993).
14. Hinrichsen, D. and A. J. Pritchard, 'Stability radii of systems with stochastic uncertainty and their optimization by output feedback', SIAM J. Control Optim., 34, 1972-1998 (1996).
15. Dragan, V., A. Halanay and A. Stoica, 'An LMI solution to a disturbance attenuation problem with state feedback for stochastic systems', Rev. Roum. Sci. Techn.-Electrotech. et Energ., 41, 513-519 (1996).
16. Hinrichsen, D. and N. K. Son, 'Stability radii of linear discrete-time systems and symplectic pencils', Int. J. Robust Nonlinear Control, 1, 79-97 (1991).
17. El Bouhtouri, A. and A. J. Pritchard, 'Stability radii of linear systems with respect to stochastic perturbation', Systems Control Lett., 19, 29-33 (1992).
18. Morozan, T., 'Stability radii for some stochastic differential equations', Stochastics Stochastics Rep., 54, 281-291 (1995).
19. ∞ control', Inter. J. Robust Nonlinear Control, 4, 421-448 (1994).
20. ∞-control for discrete-time infinite-dimensional stochastic bilinear systems', Report 08/95 National Laboratory for Scientific Computation LNCC, Rio de Janeiro 1995.
21. ∞ control problem: LMI existence conditions and state space formulas', Automatica, 30, 1307-1317 (1994).
22. Davis, M., Linear Estimation and Stochastic Control, Chapman & Hall, London, 1977.
23. Morozan, T., 'Stabilization of some stochastic discrete-time control systems', Stochastics Anal. Appl., 1, 89-116 (1983).
24. Has'minskii, R. Z., Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980 (translation of the Russian edition, Moscow, Nauka 1969).
25. Hinrichsen, D. and A. J. Pritchard, 'Real and complex stability radii: a survey', in Control of Uncertain Systems, Progress in System and Control Theory, D. Hinrichsen and B. Mårtensson (Eds), Vol. 6, Birkhäuser, Basel, 1990, pp. 119-162.
26. ∞ type control for discrete-time stochastic systems', Technical Report Nr. 424, Inst. f. Dynamische Systems, Universität Bremen, 1998.