String stability of singularly perturbed stochastic systems



Abstract

The sufficient conditions of string stability of singularly perturbed, nonlinear stochastic systems are established. The excitations are assumed to be parametric white noise. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure and the perturbation parameter e. An example is given to illustrate the results.


1. R.C. Chu, Decentralized control of high vehicle strings, Transportation Res. 8 (1974), 361-383.
2. M. Corless, L. Glielmo, On exponential stability of singularly perturbed systems, SIAM J. Contr. Optim. 30 (1998), 375-405.
3. J. Eyre, D. Yanakiev, I. Kanellakopoulos, A simplified framework for string stability analysis of automated vehicles, Veh. Sys. Dyn. 30 (1998), 375-405.
4. R.Z. Khasminski, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, the Netherlands, 1980.
5. A.A. Martynyuk, Qualitative analysis of stochastic singularly perturbed systems, Neural, Parallel & Scientific Computations 7 (1999), 211-234.
6. L. Socha, Exponential stability of singularly perturbed stochastic systems, IEEE Trans. Autom. Control 45 (2000), 576-580.
7. L. Socha, String stability of stochastic composite systems, Proceedings of CDC-2000, CD-ROM, Paper No 2885.
8. D. Swaroop, J.K. Hedrick, String stability of interconnected systems, IEEE Trans. Autom. Control, AC-41 (1996), 349-356.
Download

Published : 2003-01-30


Rybarska-RusinekL. (2003). String stability of singularly perturbed stochastic systems. Annales Mathematicae Silesianae, 16, 43-55. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14107

Liliana Rybarska-Rusinek 
Katedra Matematyki, Politechnika Rzeszowska im. Ignacego Łukasiewicza  Poland



The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.