Skip to main content

A liapunov-like criterion and a first passage-time problems in non-linear stochastic systems

  • Stochastic Control
  • Conference paper
  • First Online:
System Modeling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 38))

  • 316 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.S. Bucy: Stability and Positive Supermartingales, J. Diff. Eqs., vol.1, pp.151–155, (1965).

    Google Scholar 

  2. H.J. Kushner: Stochastic Stability and Control, Academic, N.Y. (1967).

    Google Scholar 

  3. F. Kozin: A Survey of Stability of Stochastic Systems, Automatica, vol.5, pp.95–112, Pergamon Press, (1969).

    Google Scholar 

  4. R.Z. Has'minskii: Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Maryland, (1980).

    Google Scholar 

  5. I.F. Blake and W.C. Lindsey: Level-Crossing Problems for Random Processes, IEEE Trans. Inf. Th., vol.IT-19, no.3, pp.295–315, (1973).

    Google Scholar 

  6. D.A. Darling and A.J.F. Siegert: The First Passage Problems for a Continuous Markov Process, Ann. Math Stat., vol.24, pp.624–639, (1953).

    Google Scholar 

  7. F. Kozin and S. Sugimoto: Determining Stability Properties of Stochastic Systems from Sample Observation, Proc. 1977 JACC, pp.1049–1055, (1977).

    Google Scholar 

  8. F. Kozin and S. Sugimoto: Decision Criteria for Stability of Stochastic Systems, Stochastic Problems in Dynamics, ed. by B.L. Clarkson, pp.8–35, Pitman, London, (1977).

    Google Scholar 

  9. Y. Sunahara: Stochastic Systems Theory, Inst. Electr. and Com. Eng. of Japan, Tokyo, in Japanese, (1979).

    Google Scholar 

  10. C.B. Mehr and J.A. Mcfadden: Certain Properties of Gaussian Processes and their First Passage Times, J. Roy. Statist. Soc. (B), pp.505–522, (1965).

    Google Scholar 

  11. I.I Gihman and A.V. Skorohod: Stochastic Differential Equations, Springer, N.Y., (1972).

    Google Scholar 

  12. R.Z. Khas'minskii: Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems, Th. Prob. Appls., vol.1. pp.144–147, (1967).

    Google Scholar 

  13. F. Kozin and S. Prodromou: Necessary and Sufficient Conditions for the Almost Sure Sample Stability of Linear Ito Equations, SIAM J. Appl. Math., vol.21, no.3, pp.413–424, (1971).

    Google Scholar 

  14. S. Sugimoto and F. Kozin: Some Properties on First Order Ito Systems and its Application to Finite Time Stochastic Stability Studies, Proc. 5th SICE Symp. on Contr. Th., pp.167–170, Hachioji, Tokyo, (1976).

    Google Scholar 

  15. S. Sugimoto: Relation between Sample and Moment Stability and Related Topics, Ph. D. Thesis, Dept. of Electr. Eng., Polytech. Inst. of New York, (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

R. F. Drenick F. Kozin

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Sugimoto, S. (1982). A liapunov-like criterion and a first passage-time problems in non-linear stochastic systems. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006164

Download citation

  • DOI: https://doi.org/10.1007/BFb0006164

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11691-2

  • Online ISBN: 978-3-540-39459-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics