Skip to main content
SpringerLink
Log in

Block-Diagonal Matrix-Valued Lyapunov Function and Stability of an Uncertain Impulsive System

  • Published:
International Applied Mechanics Aims and scope

Abstract

The strict (not asymptotic) stability of a nonlinear impulsive system with uncertain parameters is analyzed. New sufficient stability conditions are established based on a block-diagonal matrix-valued function. These conditions are proved to be less conservative than those established earlier

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. M. S. Branicky, “Stability of switched and hybrid systems,” in: Proc. 33rd Conf. on Decision and Control (1994), pp. 3498-3503.

  2. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).

    Google Scholar 

  3. V. Lakshmikantham and J. V. Devi, “Strict stability criteria for impulsive differential systems,” Nonlin. Anal., 21, No. 10, 785–794 (1993).

    Google Scholar 

  4. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York (1989).

    Google Scholar 

  5. Z. Li, C. B. Soh, and X. Xu, “Stability of hybrid dynamic systems,” Int. J. Syst. Sci., 28, 837–846 (1997).

    Google Scholar 

  6. T. A. Luk'yanova and A. A. Martynyuk, “Estimation of the robust stability bound for a discrete system,” Int. Appl. Mech., 38, No. 2, 231–239 (2002).

    Google Scholar 

  7. A. A. Martynyuk, Qualitative Methods of Nonlinear Dynamics. Novel Approaches to Liapunov Matrix Functions, Marcel Dekker, New York (2002).

    Google Scholar 

  8. A. A. Martynyuk and V. G. Miladzhanov, “Stability of singularly perturbed systems with structural perturbations. General theory,” Int. Appl. Mech., 39, No. 4, 375–401 (2003).

    Google Scholar 

  9. Yu. A. Martynyuk-Chernienko, “On the stability of motion of uncertain systems,” Int. Appl. Mech., 35, No. 2, 212–216 (1999).

    Google Scholar 

  10. Yu. A. Martynyuk-Chernienko, “Application of the canonical Liapunov function in the stability theory of uncertain systems,” Int. Appl. Mech., 36, No. 8, 1112–1118 (2000).

    Google Scholar 

  11. A. A. Martynyuk and L. N. Chernetskaya, “A note on the theory of stability of impulsive systems with structural perturbations,” Int. Appl. Mech., 39, No. 3, 350–355 (2003).

    Google Scholar 

  12. K. M. Passion, A. N. Michel, and P. J. Antsaklis, “Lyapunov stability of a class of discrete event systems,” IEEE Trans. on Automatic Control, 39, 269–279 (1994).

    Google Scholar 

  13. S. Pettersson and B. Lennartson, “Stability and robustness for hybrid systems,” Proc. 35th Conf. on Decision and Control (1996), pp. 1202-1207.

  14. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    A. A. Martynyuk

Authors
  1. A. A. Martynyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martynyuk, A.A. Block-Diagonal Matrix-Valued Lyapunov Function and Stability of an Uncertain Impulsive System. International Applied Mechanics 40, 322–327 (2004). https://doi.org/10.1023/B:INAM.0000031916.35045.65

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:INAM.0000031916.35045.65

Search

Navigation