Advertisement

On the solution and the moments of linear systems with randomly disturbed parameters

  • A. Kistner
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)

Abstract

By means of the considerations described above it was tried to contribute to the theory of systems the parameters of which are excited by real physical noise. It is obvious that even in the linear case many questions remain to be answered and that in most cases we are still far from methods which may be used with acceptable expense in practical applications. However the difficulties pointed out with the usual white noise approximations require further research on real noise systems.

Keywords

White Noise Stochastic Differential Equation Spectral Density Function Stochastic Differential Equa White Noise Excitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ariaratnam, S.T., Stability of Mechanical Systems under Stochastic Parameter Excitation. Lecture Notes Math. 294 (1972).Google Scholar
  2. [2]
    Bolotin, V.V., Reliability Theory and Stochastic Stability. Study No.6 Stability, Solid Mechanics Division, University of Waterloo (Ontario, Canada) (1971).Google Scholar
  3. [3]
    Zeman, J.L., Zur Lösung nichtlinearer stochastischer Probleme in der Mechanik. Acta mech. 14, 157–169 (1972).Google Scholar
  4. [4]
    Kistner, A., Über die Güte von Näherungsverfahren zur Untersuchung der Momentenstabilität farbig verrauschter Systeme. Z. angew. Math. Mech. 57, T75–T77 (1977).Google Scholar
  5. [5]
    Brockett, R.W., Finite Dimensional Linear Systems. Wiley, New York (1970).Google Scholar
  6. [6]
    Kistner, A., Strenge Aussagen über Lösung, Momente und Stabilität linearer Systeme mit Parametererregung durch farbiges Rauschen. Dissertation, Stuttgart (1978).Google Scholar
  7. [7]
    Sagle, A.A., Walde, R.E., Introduction to Lie Groups and Lie Algebras. Academic Press, New York (1973).Google Scholar
  8. [8]
    Arnold, A., Stochastische Differentialgleichungen. Oldenbourg, München (1973).Google Scholar
  9. [9]
    Willems, J.L., Aeyels, D., An Equivalence Result for Moment Stability Criteria for Parametric Stochastic Systems and Itô Equations. Internat. J. Systems Sci. 7, 577–590 (1976).Google Scholar
  10. [10]
    Lancaster, P., Theory of Matrices. Academic Press, New York (1969).Google Scholar
  11. [11]
    Mitchell, R.R., Kozin, F., Sample Stability of Second Order Linear Differential Equations with Wide Band Coefficients. SIAM J. appl. Math. 27, 571–605 (1974).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • A. Kistner
    • 1
  1. 1.Institut A für MechanikUniversität StuttgartStuttgart 80

Personalised recommendations