Stochastic H∞

SIAM Journal on Control and Optimization

Volumn 36, Issue 5, 1998, Pages 1504-1538

  Hinrichsen, D ^a   Pritchard, A J ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Bounded real lemma; H control; Matrix inequalities; State dependent noise; Stochastic systems

Indexed keywords

DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; STOCHASTIC CONTROL SYSTEMS; SYSTEM STABILITY;

BOUNDED REAL LEMMA; MATRIX INEQUALITIES; PERTURBATIONS;

CONTROL THEORY;

EID: 0032166437     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996301336     Document Type: Review

References (30)

1. L. ARNOLD, Stochastic Differential Equations: Theory and Applications, John Wiley, New York, 1974.
2. A. EL BOUHTOURI AND A. J. PRITCHARD, Stability radii of linear systems with respect to stochastic perturbations, Systems Control Lett., 19 (1992), pp. 29-33.
3. A. EL BOUHTOURI 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 (1993), pp. 475-484.
4. G. DA PRATO AND J. ZABCZYK, Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, MA, 1992.
5. ∞ control problem, IEEE Trans. Automat. Control, AC-34 (1989), pp. 831-847.
6. L. EL GHAOUI, State-feedback control of systems with multiplicative noise via linear matrix inequalities, Systems Control Lett., 24 (1995), pp. 223-228.
7. A. FRIEDMAN, Stochastic Differential Equations and Applications, Probability and Mathematical Statistics 28, Academic Press, New York, 1975.
8. ∞ control, Internat. J. Robust Nonlinear Control, 4 (1994), pp. 421-448.
9. M. GREEN AND D. J. N. LIMEBEER, Linear Robust Control, Prentice-Hall, Englewood Cliffs, NJ, 1995.
10. R. Z. HAS'MINSKII, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980. (Translation of Russian edition, Nauka, Moscow, 1969.)
11. U. G. HAUSSMANN, Optimal stationary control with state and control dependent noise, SIAM J. Control Optim., 9 (1971), pp. 184-198.
12. D, HINRICHSEN AND A. J. PRITCHARD, Stability radius for structured perturbations and the algebraic Riccati equation, Systems Control Lett., 8 (1986), pp. 105-113.
13. D. HINRICHSEN AND A. J. PRITCHARD, Riccati equation approach to maximizing the complex stability radius by state feedback, Internat. J. Control, 52 (1990), pp. 769-794.
14. D. HINRICHSEN AND A. J. PRITCHARD, Real and complex stability radii: A survey, in Control of Uncertain Systems, Progress in System and Control Theory 6, D. Hinrichsen and B. Martensson, eds., Birkhäuser, Basel, 1990, pp. 119-162.
15. D. HINRICHSEN AND A. J. PRITCHARD, Stability margins for systems with deterministic and stochastic uncertainty in Proc. 33rd IEEE Conf. Decision and Control, Florida, 1994, IEEE Computer Society Press, Los Alamitos, CA, pp. 3825-3836.
16. D. HINRICHSEN AND A. J. PRITCHARD, Stability radii of systems with stochastic uncertainty and their optimization by output feedback, SIAM J. Control Optim., 34 (1996), pp. 1972-1998.
17. ∞ control problem: LMI existence conditions and state space formulas, Automatica, 30 (1994), pp. 1307-1317.
18. N. V. KRYLOV, Introduction to the Theory of Diffusion Processes, Translations of Mathematical Monographs 142, AMS, Providence, RI, 1995.
19. N. V. KRYLOV, Controlled Diffusion Processes, Springer-Verlag, New York, 1980.
20. P. J. MCLANE, Optimal stochastic control of linear systems with state and control-dependent disturbances, IEEE Trans. Automat. Control, AC-16 (1971), pp. 292-299.
21. T. MOROZAN, Stability radii for some stochastic differential equations, Stochastics, Stochastics Rep., 54 (1995), pp. 281-291.
22. T. MOROZAN, Parametrized Riccati Equations Associated to Input-Output Operators for Time-Varying Stochastic Differential Equations with State-Dependent Noise, Institutul de Matematica al Academiei Romane, preprint no. 37, Bucarest, 1995.
23. A. PACKARD, P. ZHOU, P. PANDEY, AND G. BECKER, A collection of robust control problems leading to LMIs, in Proc. 30th IEEE Conf. Decision and Control, Brighton 1991, IEEE Comput. Society Press, Los Alamitos, CA, pp. 1245-1250.
24. L. QIU, B. BERNHARDSSON, A. RANTZER, E. J. DAVISON, P. M. YOUNG, AND J. C. DOYLE, On the real structured stability radius, in Proc. 12th IFAC World Congress, IFAC, Sydney, Australia, 1993, pp. 71-78.
25. ∞ optimization without assumptions on finite or infinite zeros, SIAM J. Control Optim., 30 (1992), pp. 123-142.
26. ∞ Control Problem, Prentice-Hall, New York, 1992.
27. J. L. WILLEMS AND J. C. WlLLEMS, Feedback stabilizability for stochastic systems with state and control dependent noise, Automatica, 12 (1976), pp. 277-283.
28. J. WILLEMS AND J. C. WILLEMS, Robust stabilization of uncertain systems, SIAM J. Control Optim., 21 (1983), pp. 352-374.
29. W. M. WONHAM, Optimal stationary control of a linear system with state dependent noise, SIAM J. Control Optim., 5 (1967), pp. 486-500.
30. W. M. WONHAM, Random differential equations in control theory, in Probabilistic Methods in Applied Mathematics, 2, A. T. Bharucha-Reid, ed., Academic Press, New York, 1970, pp. 131-212.