Uniform eventual practical stability of impulsive differential system in terms of two measures
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DOI:
https://doi.org/10.26637/MJM0702/0015Abstract
In the present paper, an impulsive differential system is investigated for uniform eventual practical stability. Sufficient criteria have been obtained for the uniform eventual practical stability of the impulsive differential system in terms of two measures by using Lyapunov-like function. The results that are obtained to investigate the stability are significantly dependent on the impulse moments. The results have been verified with the help of an example
Keywords:
Impulsive differential system, Eventual Practical Stability, Two Measures, Lyapunov functionMathematics Subject Classification:
Mathematics- Pages: 245-250
- Date Published: 01-04-2019
- Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)
W. Feng and X. Fu, Eventual Stability in Terms of Two Measures of Nonlinear Differential Systems, Vietnam Journal of Mathematics, 28(2000), 143-151.
J. Henderson and S. Hristova, Eventual Practical Stability and cone valued Lyapunov functions for differential equations with maxima, Communications in Applied Analysis, $14(2010), 515-524$.
T. Kostadinov and K. Ivanova, Eventual Stability with two measures for nonlinear differential equations with non-instantaneous impulses, International Journal of Pure and Applied Mathematics, 116(2017), 751-764.
V. Lakshmikantham and D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, vol. 6. World Scientific, 1989.
V. Lakshmikantham and X. Liu, Stability Criteria for Impulsive Differential Equations in Terms of Two Measures, Journal of Mathematical Analysis and Applications, 137(1988), 591-604.
J. P. La Salle and R. J. Rath, Eventual Stability, vol. 6 . Elsevier, 1964.
X. Liu and G. Baliinger, Uniform Asymptotic Stability of Impulsive Delay Differential Equations, Computers and Mathematics with Applications, 41(2001), 903-915.
X. Liu and Q. Wang, On stability in terms of two measures for impulsive systems of functional differential equations, Journal of Mathematical Analysis and Applications, $326(2007), 252-265$.
J.H. Shen, Razumikhin techniques in impulsive functional differential equations, Nonlinear Analysis, $36(1999), 119-130$.
P. Singh and S. K. Srivastava and K. Kaur, Uniform practical stability in terms of two measures with effect of delay at the time of impulses, Nonlinear Engineering, 5(2016), 93-97.
A. A. Soliman, Stability criteria of impulsive differential systems, Applied Mathematics and Computation, $134(2003), 445-457$
I. M. Stamova, Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations, Journal of Mathematical Analysis and Applications, $325(2007), 612-623$.
I. M. Stamova and G. T. Stamov, Lyapunov Razumikhin method for impulsive functional differential equations and applications to the population dynamics, Journal of Computational and Applied Mathematics, 130(2001), $163-171$
Q. Wang and X. Liu, Exponential stabilityfor impulsive delay differential equations by Razumikhin method, Journal of Mathematical Analysis and Applications, $309(2005), 462-473$.
Y. Zhang and J. Sun, Practical Stability of Impulsive Functional Differential Equations in Terms of Two Measurements, Computers and Mathematics with Applications, $48(2004), 1549-1556$.
Y. Zhang and J. Sun, Eventual practical stability of impulsive differential equations with time delay in terms of two measurements, Journal of Computational and Applied Mathematics, 176(2005), 223-229.
Y. Zhang and J. Sun, Eventual Stability of Impulsive Differential systems, Acta Mathematica Scientia, 27B(2007), $373-380$.
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