Stochastic uniform observability of linear differential equations with multiplicative noise

Journal of Mathematical Analysis and Applications

Volumn 343, Issue 1, 2008, Pages 446-463

  Ungureanu, Viorica Mariela ^a  

^a Universitatea Constantin Brancusi din Targu Jiu   (Romania)

Author keywords

Covariance operators; Hilbert Schmidt spaces; Perturbed evolution operators; Stochastic differential equations; Stochastic uniform observability

Indexed keywords

EID: 41549141852     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.01.058     Document Type: Article

References (20)

1. Curtain R., and Pritchard J. Infinite Dimensional Linear Systems Theory (1978), Springer-Verlag, Berlin
2. Dragan V., and Morozan T. Stochastic observability and applications. IMA J. Math. Control Inform. 21 (2004) 323-344
3. Gelfand I., and Vilenkin H. Generalized Functions, Part 4 (1964), Springer-Verlag, Berlin
4. Germani A., Jetto L., and Piccioni M. Galerkin approximations for optimal linear filtering of infinite-dimensional linear systems. SIAM J. Control Optim. 26 (1988) 1287-1305
5. Grecksch W., and Tudor C. Stochastic Evolution Equations: A Hilbert Space Approach. Math. Res. vol. 75 (1995), Akademie-Verlag, Berlin
6. Kalman R.E. Contributions to theory of optimal control. Bol. Soc. Mat. Mexicana 5 (1960) 102-119
7. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci. vol. 44 (1983), Springer-Verlag, Berlin
8. Da Prato G. Quelques resultats d'existence, unicite et regularite pour une probleme de la theorie du controle. J. Math. Pures Appl. 52 (1973) 353-375
9. Da Prato G., and Ichikawa A. Quadratic control for linear time-varying systems. SIAM J. Control Optim. 28 2 (1990) 359-381
10. Da Prato G., and Ichikawa A. Quadratic control for linear periodic systems. Appl. Math. Optim. 18 (1988) 39-66
11. Da Prato G., and Zabczyc J. Stochastic Equations in Infinite Dimensions (1992), Cambridge University Press, Cambridge
12. Da Prato G., and Ichikawa A. Lyapunov equations for time-varying linear systems. Systems Control Lett. 9 (1987) 165-172
13. Morozan T. Stochastic uniform observability and Riccati equations of stochastic control. Rev. Roumaine Math. Pures Appl. 38 9 (1993) 771-781
14. Morozan T. On the Riccati Equation of Stochastic Control. Internat. Ser. Numer. Math. vol. 107 (1992), Birkhäuser, Basel
15. Morozan T. Linear quadratic control and tracking problems for time-varying stochastic differential systems perturbed by a Markov chain. Rev. Roumaine Math. Pures Appl. 46 6 (2001) 783-804
16. Ungureanu V.M. Riccati equation of stochastic control and stochastic uniform observability in infinite dimensions. In: Barbu V., Lasiecka I., Tiba D., and Varsan C. (Eds). Analysis and Optimization of Differential Systems (2003), Kluwer Academic Publishers 421-423
17. Ungureanu V.M. Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems. Electron. J. Qual. Theory Differ. Equ. 4 (2004) 1-22
18. Ungureanu V.M. Cost of tracking for differential stochastic equations in Hilbert spaces. Studia Univ. Babes-Bolyai Math. L 4 (2005) 73-83
19. Tudor C. Optimal control for an infinite-dimensional periodic problem under white noise perturbations. SIAM J. Control Optim. 28 2 (1990) 253-264
20. Zabczyk J. On optimal stochastic control of discrete-time systems in Hilbert space. SIAM J. Control Optim. 13 6 (1975) 1217-1234