Stochastic stabilization of differential systems with general decay rate

Systems and Control Letters

Volumn 48, Issue 5, 2003, Pages 397-406

  Caraballo, Tomás ^a   Garrido Atienza, María J ^a   Real, José ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Cylindrical Wiener process; General decay rate; Ito's noise; Pathwise stability of stochastic systems; Stabilization

Indexed keywords

LYAPUNOV METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; SYSTEM STABILITY;

DIFFERENTIAL SYSTEMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 0037445785     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(02)00293-1     Document Type: Article

References (15)

1. Arnold L. Stabilization by noise revisited. Z. Angew. Math. Mech. 70:1990;235-246.
2. Arnold L., Crauel H., Wihstutz V. Stabilization of linear systems by noise. SIAM J. Control Optim. 21:1983;451-461.
3. Caraballo T., Garrido-Atienza M.J., Real J. Existence and uniqueness of solutions for delay stochastic evolution equations. Stochastic Anal. Appl. 20(6):2002;1225-1255.
4. Caraballo T., Langa J.A. Comparison of the long-time behavior of linear Ito and Stratonovich partial differential equations. Stochastic Anal. Appl. 19(2):2001;183-195.
5. Caraballo T., Liu K., Mao X.R. On stabilization of partial differential equations by noise. Nagoya Math. J. 161(2):2001;155-170.
6. Da Prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge University Press, London.
7. Has'minskii R. Stochastic Stability of Differential Equations. 1980;Sijthoff and Noordhoff, Netherlands.
8. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod Gauthier-Villars, Paris, 1969.
9. Liu K., Mao X.R. Large time decay behavior of dynamical equations with random perturbation features. Stochastic Anal. Appl. 19(2):2001;295-327.
10. Mao X.R. Almost sure polynomial stability for a class of SDEs. Quart. J. Math. Oxford Ser. (2). 43:1992;339-348.
11. Mao X.R. Stochastic stabilization and destabilization. Systems & Control Lett. 23:1994;279-290.
12. Mao X.R. Exponential Stability of Stochastic Differential Equations. 1994;Marcel Dekker, New York.
13. X.R. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, 1997.
14. E. Pardoux, Équations aux dérivées partielles stochastiques non linéaires monotones, Thèse, Université Paris XI, 1975.
15. Scheutzow M. Stabilization and destabilization by noise in the plane. Stochastic Anal. Appl. 11(1):1993;97-113.