I -Eventual Stability of Differential Systems with Impulses

1
Anju Sood
Anju Sood
2
Sanjay K Srivastava
Sanjay K Srivastava
1 Punjab Technical University, Kapurthala(Punjab)-INDIA

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In our paper, we have established criterion of Ψ-Eventual Stability for impulsive differential systems with variable moments of impulses by using piecewise continuous auxiliary functions which are analogous to Lyapunov’s functions. The work of Bainov, Kulev and Soliman has been extended. An example has been given to support the theoretical result. In the example, the zero solution is not stable in the sense of Lyapunov but it is uniformly eventually stable. Moreover a weight function Ψ is also associated with state vectors.

8 Cites in Articles

References

  1. G Kulev,D Bainov (1988). Asymptotic stability of systems with impulses by the direct method of Lyapunov.
  2. Diamandescu (2005). On the Ψ-stability of a nonlinear volterra integro differential systems.
  3. Aurel Diamandescu (2008). On the ψ-exponential asymptotic stability of nonlinear systems of differential equations.
  4. J Morchalo (1990). On (Ψ-Lp) stability of nonlinear systems of differential equations.
  5. A Soliman (2003). Stability criteria of impulsive differential systems.
  6. Anju Sood,S Srivastava (2012). New conditions for stability of solution of impulsive differential equations.
  7. Yu Zhang,Jitao Sun (2007). Eventual stability of impulsive differential systems.
  8. Yu Zhang,Jitao Sun (2007). Eventual stability of impulsive differential systems.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Anju Sood. 2014. \u201cI -Eventual Stability of Differential Systems with Impulses\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 14 (GJSFR Volume 14 Issue F6): .

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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October 29, 2014

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English

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In our paper, we have established criterion of Ψ-Eventual Stability for impulsive differential systems with variable moments of impulses by using piecewise continuous auxiliary functions which are analogous to Lyapunov’s functions. The work of Bainov, Kulev and Soliman has been extended. An example has been given to support the theoretical result. In the example, the zero solution is not stable in the sense of Lyapunov but it is uniformly eventually stable. Moreover a weight function Ψ is also associated with state vectors.

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I -Eventual Stability of Differential Systems with Impulses

Anju Sood
Anju Sood Punjab Technical University, Kapurthala(Punjab)-INDIA
Sanjay K Srivastava
Sanjay K Srivastava

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