Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-15T05:40:38.463Z Has data issue: false hasContentIssue false
  • English
  • Français

The method of V. M. Popov for differential systems with random parameters

Published online by Cambridge University Press:  14 July 2016

Chris P. Tsokos
Chris P. Tsokos*
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
Get accessRights & Permissions [Opens in a new window]

Abstract

The aim of this paper is to investigate the existence of a random solution and the stochastic absolute stability of the differential systems (1.0)–(1.1) and (1.2)–(1.3) with random parameters. These objectives are accomplished by reducing the differential systems into a stochastic integral equation of the convolution type of the form (1.4) and utilizing a generalized version of V. M. Popov's frequency response method.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971, pp. 298 - 310
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Morozan, T. (1967) Stability of some linear stochastic systems. J. Differential Equations 3, 153–169.Google Scholar
[2] Morozan, T. (1967) Stability of linear systems with random parameters. J. Differential Equations 3, 170–178.Google Scholar
[3] Barbalat, I. (1959) Systèmes d'équations differentielles d'oscillations non-linéar. Rev. Math. Pures. Appl. 4, 267–270.Google Scholar
[4] Halanay, A. (1966) Differential Equation-Stability Oscillations , Time Lags. Academic Press, New York. 513–514.Google Scholar
[5] Bochner, S. (1959) Lectures on Fourier integrals. Ann. Math. 42, 217–218.Google Scholar
[6] Morozan, T. (1966) The method of V. M. Popov for control systems with random parameters. J. Math. Anal. Appl. 16, 201–215.Google Scholar
[7] Titchmarsh, E. C. (1959) Introduction to the Theory of Fourier Integrals. Clarendon Press, Oxford.Google Scholar
[8] Tsokos, C. P. (1969) On a stochastic integral equation of the Volterra type. Math. Systems Theory 3, 222–231.Google Scholar