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Volumn 53, Issue 3, 2008, Pages 683-691

Stabilization and destabilization of nonlinear differential equations by noise

Author keywords

Almost sure asymptotic stability; Brownian motion; Destabilization; It 's formula; Stabilization

Indexed keywords

ASYMPTOTIC STABILITY; BROWNIAN MOVEMENT; PERTURBATION TECHNIQUES;

EID: 42649104364     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.919255     Document Type: Article
Times cited : (193)

References (27)
  • 1
    • 84863352148 scopus 로고    scopus 로고
    • Stabilization of functional differential equations by noise
    • to be published
    • J. A. D Appleby, "Stabilization of functional differential equations by noise," Syst. Cont. Lett. to be published.
    • Syst. Cont. Lett
    • Appleby, J.A.D.1
  • 2
    • 42649112564 scopus 로고    scopus 로고
    • Destabilization of functional differential equations by noise
    • to be published
    • J. A. D Appleby, "Destabilization of functional differential equations by noise," Systems Control Lett. to be published.
    • Systems Control Lett
    • Appleby, J.A.D.1
  • 3
  • 4
    • 24944579472 scopus 로고    scopus 로고
    • Stochastic stabilisation of functional differential equations
    • J. A. D. Appleby and X. Mao, "Stochastic stabilisation of functional differential equations," Syst. Control Lett., vol. 54, no. 11, pp. 1069-1081, 2005.
    • (2005) Syst. Control Lett , vol.54 , Issue.11 , pp. 1069-1081
    • Appleby, J.A.D.1    Mao, X.2
  • 6
    • 0020749018 scopus 로고
    • Stabilization of linear systems by noise
    • L Arnold, H. Crauel, and V. Wihstutz, "Stabilization of linear systems by noise," SIAM J. Control Optim., vol. 21, pp. 451-461, 1983.
    • (1983) SIAM J. Control Optim , vol.21 , pp. 451-461
    • Arnold, L.1    Crauel, H.2    Wihstutz, V.3
  • 8
    • 0037445785 scopus 로고    scopus 로고
    • Stochastic stabilization of differential systems with general decay rate
    • T. Caraballo, M. Garrido-Atienza, and J. Real, "Stochastic stabilization of differential systems with general decay rate.," Syst. Control Lett., vol. 48, pp. 397-406, 2003.
    • (2003) Syst. Control Lett , vol.48 , pp. 397-406
    • Caraballo, T.1    Garrido-Atienza, M.2    Real, J.3
  • 9
    • 3142766206 scopus 로고    scopus 로고
    • Stabilization of linear PDEs by Strotonovich noise
    • T Caraballo and J.C Robinson, "Stabilization of linear PDEs by Strotonovich noise," Syst. Control Lett., vol. 53, pp. 41-50, 2004.
    • (2004) Syst. Control Lett , vol.53 , pp. 41-50
    • Caraballo, T.1    Robinson, J.C.2
  • 10
    • 84863354512 scopus 로고    scopus 로고
    • The effect of noise on the Chafee-Infante equation: A nonlinear case study
    • to be published
    • Caraballo, H. Crauel, J.A. Langa, and J.C. Robinson, "The effect of noise on the Chafee-Infante equation: A nonlinear case study," Proc. AMS, to be published.
    • Proc. AMS
    • Caraballo1    Crauel, H.2    Langa, J.A.3    Robinson, J.C.4
  • 14
    • 0000427961 scopus 로고
    • On the stability of processes defined by stochastic difference-differential equations
    • H.J. Kushner, "On the stability of processes defined by stochastic difference-differential equations," J. Differ. Equ., vol. 4, pp. 424-443, 1968.
    • (1968) J. Differ. Equ , vol.4 , pp. 424-443
    • Kushner, H.J.1
  • 15
    • 0028438592 scopus 로고
    • Vibrational contiol of nonlinear time lag systems with bounded delay: Averaging theory, stabilizability, and transient behavior
    • May
    • B. Lehman, J. Bentsman, S. V. Lunel, and E. I. Verriest, "Vibrational contiol of nonlinear time lag systems with bounded delay: Averaging theory, stabilizability, and transient behavior," IEEE Trans. Autom. Control, vol. 39, no. 5, pp. 898-912, May 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.5 , pp. 898-912
    • Lehman, B.1    Bentsman, J.2    Lunel, S.V.3    Verriest, E.I.4
  • 18
    • 0028518403 scopus 로고
    • Stochastic siabilisation and destabilization
    • X. Mao, "Stochastic siabilisation and destabilization," Syst. Control Lett., vol. 23, pp. 279-290, 1994.
    • (1994) Syst. Control Lett , vol.23 , pp. 279-290
    • Mao, X.1
  • 20
    • 33845950815 scopus 로고    scopus 로고
    • Stabilization and destabilization of hybrid systems of stochastic differential equations
    • X. Mao, G. G. Yin, and C. Yuan, "Stabilization and destabilization of hybrid systems of stochastic differential equations," Automatica, vol. 43, pp. 264-273, 2007.
    • (2007) Automatica , vol.43 , pp. 264-273
    • Mao, X.1    Yin, G.G.2    Yuan, C.3
  • 21
    • 0020112869 scopus 로고
    • Condition of virbrational stablizability for a class of non-linear systems
    • Apr
    • S. Meerkov, "Condition of virbrational stablizability for a class of non-linear systems," IEEE Trans. Autom. Control, vol. 27, no. 2, pp. 485-487, Apr. 1982.
    • (1982) IEEE Trans. Autom. Control , vol.27 , Issue.2 , pp. 485-487
    • Meerkov, S.1
  • 24
    • 0002900926 scopus 로고
    • Stabilization and destabilization by noise in the plane
    • M. Scheutzow, "Stabilization and destabilization by noise in the plane," Stoch. Anal. Appl., vol. 11, no. 1, pp. 97-113, 1993.
    • (1993) Stoch. Anal. Appl , vol.11 , Issue.1 , pp. 97-113
    • Scheutzow, M.1
  • 25
    • 42649102155 scopus 로고
    • Hyperbolic PDE's, randomly switched systems and applications to stochastic stabilisation
    • E. I. Verriest, "Hyperbolic PDE's, randomly switched systems and applications to stochastic stabilisation," in Proc. 14th IMACS World Congr. Comput. Appl. Math., 1994, pp. 1527-1530.
    • (1994) Proc. 14th IMACS World Congr. Comput. Appl. Math , pp. 1527-1530
    • Verriest, E.I.1
  • 26
    • 0025549362 scopus 로고
    • On a hyperbolic PDE describing the forward evolution of a class of randomly alternating systems
    • Honolulu, HI
    • E. I. Verriest, "On a hyperbolic PDE describing the forward evolution of a class of randomly alternating systems," in Proc. 29th IEE Conf. Decis. Control, Honolulu, HI, 1990, pp. 2147-2148.
    • (1990) Proc. 29th IEE Conf. Decis. Control , pp. 2147-2148
    • Verriest, E.I.1
  • 27
    • 24944500299 scopus 로고
    • Problem of vibrational stabilisation of linear systems
    • A. P. Zhabko and V. L. Kharitonov, "Problem of vibrational stabilisation of linear systems," Autom. Telemekh., vol. 2, pp. 31-34, 1980.
    • (1980) Autom. Telemekh , vol.2 , pp. 31-34
    • Zhabko, A.P.1    Kharitonov, V.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.