Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

Dr. Dilbaj Singh; Sanjay Kumar Srivastava

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

Dr. Dilbaj Singh * §

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Sanjay Kumar Srivastava

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Lovely Professional University, Punjab, India.

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

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Abstract

Strict stability is the kind of stability that can give us some information about the rate of decay of the solution. There are some results about strict stability of functional differential equations. On other hand, in the study of stability, an interesting set of problems deal with bringing sets close to a certain state, rather than the equilibrium state. The desired state of a system may be mathematically unstable and yet the system may oscillate sufficiently near this state that its performance is acceptable. Many problems fall into this category. Such considerations led to the notion of practical stability which is neither weaker nor stronger than stability. In this paper, strict practical stability of Impulsive functional differential equations in which the state variables on the impulses are related to time delay is considered. By using Lyapunov functions and Razumikhin technique, some criteria for strict practical stability for functional differential equations, in which the state variables on the impulses are related to the time delay, are provided.

References

15 Cites in Article

Reference Format

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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. Dilbaj Singh, Sanjay Kumar Srivastava. 1970. "Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F1).

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GJSFR Volume 13 Issue F1

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

impulsive functional differential equation lyapunov function razumikhin technique strict stability time delay

Classification

GJSFR-F Classification MSC 2010: 12H20

34A09

Submission ReceivedNovember 28, 2012
Peer Review Double Blind
Handling Editor
Accepted December 19, 2012
Published January 3, 2013

Version of record

v1.2

Language

English

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Article Matrices

Total Score: 151

Country: India

Subject: Global Journal of Science Frontier Research

Authors: Dr. Dilbaj Singh, Sanjay Kumar Srivastava (PhD/Dr. count: 1)

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Publish Date: 2013 01, Thu

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