Skip to main content
SpringerLink
Log in

Stability of nonlinear comparison equations for discrete large-scale systems

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C 1 is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bailey, F.N., The application of Lyapunov's second method to interconnected systems,J. SIAM, Control Ser. A,3 (1966), 443–462.

    Google Scholar 

  2. Shu Zhong-zhou, Stability of comparison equations,Chinese Annals of Mathematics,7A, 6 (1986), 676–684. (in Chinese)

    Google Scholar 

  3. Shu Zhong-zhou, General theorems on the stability of large-scale systems,SIAM Conference on Control in the 90's, San Francisco, May (1989).

  4. Feng En-bo, Comparison principle of the discrete large-scale systems in the theory of stability and its applications,Control Theory and Applications,1, 1 (1984), 92–100.

    Google Scholar 

  5. Lasalle, J.P.,The Stability of Dynamical Systems, J.W. Arrowsmith Ltd., Bristol, 3. England (1976).

    Google Scholar 

  6. Shu, Zhong-zhou, Researches on stability of motion in China,Advances in Mechanics,18, 1 (1988), 1–12. (in Chinese)

    Google Scholar 

  7. Xu, Song-qing,Stability Theory of Ordinary Differential Equations, Shanghai Science and Technology Press, Shanghai (1962). (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Southwest Jiaotong University, Chengdu

    Shu Huang

Authors
  1. Shu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Li Li

Projects Supported by the National Natural Science Foundation of China, 1880359.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, S. Stability of nonlinear comparison equations for discrete large-scale systems. Appl Math Mech 11, 779–785 (1990). https://doi.org/10.1007/BF02015153

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02015153

Keywords

Search

Navigation