Skip to main content
Log in

Stability and Liapunov’s matrix functions method in dynamical systems

  • Published:
International Applied Mechanics Aims and scope

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

Access this article

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

Instant access to the full article PDF.

References

  1. M. Z. Djordjevic, “Stability analysis of large scale systems whose subsystems may be unstable,”Large Scale Systems, Vol.5, 252–262 (1983).

    MathSciNet  Google Scholar 

  2. Lj. T. Grujic, A. A. Martynyuk, and M. Ribbens-Pavella,Large Scale Systems Stability under Structural and Singular Perturbations, Springer Verlag, Berlin (1987).

    MATH  Google Scholar 

  3. J. X. He and M. S. Wang, “Remarks on exponential stability by comparison functions of the same order of magnitude,”Ann. of Diff Eqs.,7, No. 4, 409–414 (1991).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Martynyuk, “Liapunov matrix-function and theory of stability,”Proc. IMACS—IFAC Symp., June 3–6, IND. Villeneuve d’Ascq, France, (1986), 261–265.

  5. A. A. Martynyuk, “Qualitative analysis of nonlinear systems by the method of matrix Lyapunov functions,”Rocky Mount. J. Math.,25, 397–415 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. A. Martynyuk,Stability by Liapunov’s Matrix Functions Method with Applications, Marcel Dekker, Inc., New York (1998).

    Google Scholar 

  7. A. A. Martynyuk, “Aggregation forms of nonlinear systems. Domains of asymptotic stability,”Prikl. Mekh.,32, No. 4, 3–19 (1996).

    MathSciNet  Google Scholar 

  8. A. A. Martynyuk, V. G. Miladzhanov, and K. A. Begmuratov, “Construction of hierarchical matrix Lyapunov functions,”J. Math. Anal. Appi,185, No. 1, 129–145 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  9. N. Rouche, P. Habets, and M. Laloy,Stability Theory by Liapunov’s Direct Method, Springer-Verlag, New-York (1977).

    MATH  Google Scholar 

  10. V. I. Zubov,Mathematical Investigation of Control Systems [in Russian], Mashinostroeniye, Leningrad (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This is a part of the report on “Symposium on Comparison Methods and Stability Theory,” June 3–6,1993, Waterloo, Ontario, Canada

Translated from Prikladnaya Mekhanika, Vol. 34, No. 10, pp. 144–152, October, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martynyuk, A.A. Stability and Liapunov’s matrix functions method in dynamical systems. Int Appl Mech 34, 1057–1065 (1998). https://doi.org/10.1007/BF02701063

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02701063

Keywords

Navigation