Skip to main content
SpringerLink
Log in

A new approach to exponential stability analysis of nonlinear systems

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point-wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

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. Mohammed Aassila,Asymptotic Stability and Decay Rate of Solutions for a Nonlinear Wave Equation with Variable Coefficients, J. Appl. Math. & Computing6(1) (1999), 185–196.

    MATH  MathSciNet  Google Scholar 

  2. M. Jaroslaw,Stability Analysis of Nonlinear Difference Systems, Applied Mathematics and Computation95(1) (1998), 27–36.

    Article  MATH  MathSciNet  Google Scholar 

  3. Yuji Liu and Weigao Ge,Asymptotic Behavior of Solutions of Forced Nonlinear Neutral Difference Equations, J. Appl. Math. & Computing16 (2004), 37–52.

    Article  MATH  MathSciNet  Google Scholar 

  4. Mahmoud Gamal M., Bountis Tassos and Ahmed Sayed A,Stability Analysis for Systems of Nonlinear Hill's Equations, Physica A286(1–2) (2000), 133–146.

    Article  MATH  Google Scholar 

  5. El-Sheikh M. M. A., Soliman A. A. and Abd Alla M. H.,On Stability of Nonlinear Differential Systems via Cone-Valued Liapunov Function Method, Applied Mathematics and Computation119(2–3) (2001), 265–281.

    Article  MATH  MathSciNet  Google Scholar 

  6. Jigen Peng,Theoretical Research on Nonlinear Semigroup of Lipschitz Operators and Its Applications, Ph.D. Thesis, Xi'an Jiaotong University, 1998.

  7. Jigen Peng and Zongben Xu,On Asymptotic Behaviours of Nonlinear Semigroup of Lipschitz Operators with Applications, Acta Mathematica Sinica45(6) (2002), 1099–1106.

    MATH  MathSciNet  Google Scholar 

  8. Hong Qiao, Jigen Peng and Zongben Xu,Nonlinear Measures: A New Approach to Exponential Stability Analysis for Hopfield-Type Neural Networks, IEEE Transactions of Neural Networks12(2) (2001), 360–370.

    Article  Google Scholar 

  9. Sastry Shankar,Nonlinear System: Analysis, Stability and Control, Springer, New York, 1999.

    MATH  Google Scholar 

  10. G. Söderlind,Bounds on Nonlinear Operators in Finite-Dimensional Banach Spaces, Numer. Math.50 (1986), 27–44.

    Article  MATH  MathSciNet  Google Scholar 

  11. Thomas L. Vincent and Walter J. Grantham,Nonlinear and Optimal Control Systems, Wiley, New York, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, South China Agricultural University, 510642, Guangzhou, China

    Anhua Wan

  2. Faculty of Science, Xi'an Jiaotong University, 710049, Xi'an, China

    Anhua Wan

Authors
  1. Anhua Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anhua Wan.

Additional information

Anhua Wan received her BS and MS from Nanchang University respectively in 1998 and 2001, and since September 2001 she has been a Ph. D. candidate in Xi'an Jiaotong University, majoring in applied mathematics. Her research interests include nonlinear systems, stability theory and control theory and their applications in population dynamics, robotics etc. So far, she has published more than ten papers.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wan, A. A new approach to exponential stability analysis of nonlinear systems. JAMC 19, 345–351 (2005). https://doi.org/10.1007/BF02935809

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02935809

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation