Ψ-Eventual Stability of Differential System with Impulses
In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.
[1] A. Dimandescu, On the Ψ-stability of nonlinear voltera integro-differential systems, Electronic Journal of differential equations, 56: 1-14 (2005).
[2] A. A. Soliman, Stability criteria of impulsive differential systems, Applied Mathematics and Computation 134: 445-457 (2003).
[3] A. A. Soliman, On stability of perturbed impulsive differential systems, Applied Mathematics and Computation 133: 105-117 (2002).
[4] D. D. Bainov and P. S. Simeonov, Systems with impulse effect: Stability, Theory and Applications, Ellis Horwood, Chichester, UK, 1989.
[5] J. T. Sun, Y. P. Zhang and Q. D. Wu, Less conservative conditions for asymptotic stability of impulsive control systems, IEEE Trans Automatic Control 48(5): 829-831 (2003).
[6] J. Mochalo, On (Ψ-Lp)-stability of nonlinear systems of differential equations, Analele Stiintifice ale Universitatii Al. I. Cuza Iasi, Tomul XXXVI, s. I-a, Mathematica, f.4: 353-360 (1990).
[7] O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., (8), 65: 259-264 (1978).
[8] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, "Theory of Impulsive Differential Equations," World Scientific, Singapore / New Jersey / London, 1989.
[9] Y. Zhang and J. Sun, Boundedness of the solutions of impulsive differential systems with time-varying delay, Applied Mathematics and Computation 154: 279-288 (2004).
[10] Y. Zhang and J. Sun, Eventual Stability of Impulsive Differential Systems, Acta Mathematica Scientia 27 B: 373-380 (2002).
[11] Z. G. Luo and J. H. Shen, New Razumikhin type theorems for impulsive functional differential equations, Applied Mathematics and Computation 125: 375-386 (2002).
[1] A. Dimandescu, On the Ψ-stability of nonlinear voltera integro-differential systems, Electronic Journal of differential equations, 56: 1-14 (2005).
[2] A. A. Soliman, Stability criteria of impulsive differential systems, Applied Mathematics and Computation 134: 445-457 (2003).
[3] A. A. Soliman, On stability of perturbed impulsive differential systems, Applied Mathematics and Computation 133: 105-117 (2002).
[4] D. D. Bainov and P. S. Simeonov, Systems with impulse effect: Stability, Theory and Applications, Ellis Horwood, Chichester, UK, 1989.
[5] J. T. Sun, Y. P. Zhang and Q. D. Wu, Less conservative conditions for asymptotic stability of impulsive control systems, IEEE Trans Automatic Control 48(5): 829-831 (2003).
[6] J. Mochalo, On (Ψ-Lp)-stability of nonlinear systems of differential equations, Analele Stiintifice ale Universitatii Al. I. Cuza Iasi, Tomul XXXVI, s. I-a, Mathematica, f.4: 353-360 (1990).
[7] O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., (8), 65: 259-264 (1978).
[8] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, "Theory of Impulsive Differential Equations," World Scientific, Singapore / New Jersey / London, 1989.
[9] Y. Zhang and J. Sun, Boundedness of the solutions of impulsive differential systems with time-varying delay, Applied Mathematics and Computation 154: 279-288 (2004).
[10] Y. Zhang and J. Sun, Eventual Stability of Impulsive Differential Systems, Acta Mathematica Scientia 27 B: 373-380 (2002).
[11] Z. G. Luo and J. H. Shen, New Razumikhin type theorems for impulsive functional differential equations, Applied Mathematics and Computation 125: 375-386 (2002).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58890", author = "Bhanu Gupta", title = "Ψ-Eventual Stability of Differential System with Impulses", abstract = "In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.
", keywords = "impulsive differential equations, Lyapunov function, eventual stability", volume = "5", number = "9", pages = "1500-5", }
