Strictly Practical Stabilization of Impulsive Functional Differential Equations by using Lyapunov functions

Dr. Sapna Rani

Strictly Practical Stabilization of Impulsive Functional Differential Equations by using Lyapunov functions

Dr. Sapna Rani * §

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Strictly Practical Stabilization of Impulsive Functional Differential Equations by using Lyapunov functions

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Abstract

In this paper, we extend the concept of strict practical stability to impulsive functional differential equations by using Lyapunov functions and Razumikhin technique. As practical stability does not give us much information about the rate of decay of solution so we develop the idea for strict practical stability of functional differential equations with impulsive effect and obtained some conditions for strict practical uniform stability for functional differential equations with impulse by using piecewise continuous Lyapunov functions and Razumikhin technique.

References

9 Cites in Article

Reference Format

Dilbaj Singh,S Srivastava (2012). Stability criteria of impulsive differential equations with comparison results.
Dilbaj Singh,S Srivastava (2012). Strict stability criteria for impulsive functional differential equations.
Dilbaj Singh,S Srivastava (2013). Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations.
J Lasalle,S Lefschetz (1961). Stability by Liapunov's Direct Method, with Applications.
Kaien Liu,Guowei Yang (2008). Strict Stability Criteria for Impulsive Functional Differential Systems.
S Bernfeld,V Lakshmikantam (1979). Practical Stability and Lyapunov Functions.
D Lakshmikantam,P Bainov,Simonov (1989). Theory of impulsive Differential equations.
Y Lakshmikantam,Zhang (2001). Strict Practical Stability of Delay Differential Equations.
V Lakshmikantham,S Leela,A Martynyuk (1990). Practical Stability of Nonlinear Systems.

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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.

How to Cite This Article

Dr. Sapna Rani. 2013. "Strictly Practical Stabilization of Impulsive Functional Differential Equations by using Lyapunov functions". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F4).

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GJSFR Volume 13 Issue F4

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

impulsive differential equations lyapunov function strict practical stability

Classification

GJSFR-F Classification MSC 2010: 37L45

12H20

Submission ReceivedApril 10, 2013
Peer Review Double Blind
Handling Editor
Accepted May 10, 2013
Published May 22, 2013

Version of record

v1.2

Issue date

May 25, 2013

Language

English

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Article Matrices

Total Score: 151

Country: India

Subject: Global Journal of Science Frontier Research

Authors: Dr. Sapna Rani, Dilbaj Singh (PhD/Dr. count: 1)

View Count (all-time): 321

Total Views (Real + Logic): 1278

Total Downloads (simulated): 74

Publish Date: 2013 05, Wed

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Total Views: 1.3K

Total Downloads: 74

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