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Stability criteria for impulsive systems on time scales. (English) Zbl 1142.39011
This paper deals with the asymptotic stability of impulsive systems on time scales by means of comparison theorem and Lyapunov functions. An example is included to illustrate the efficiency of the proposed results.
MSC:
39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
34A37Differential equations with impulses
References:
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[2]Bainov, D. D.; Simeonov, P. S.: Systems with impulse effect, stability theory and applications, (1989) · Zbl 0683.34032
[3]Bohner, M.; Peterson, A.: Dynamic equations on time scales: an introduction with applications, (2001)
[4]Bohner, M.; Peterson, A.: Advances in dynamic equations on time scales, (2003)
[5]Erbe, L.; Peterson, A.; Saker, S. H.: Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales, J. comput. Appl. math. 181, 92-102 (2005) · Zbl 1075.39010 · doi:10.1016/j.cam.2004.11.021
[6]Hoffacker, J.; Tisdell, C. C.: Stability and instability for dynamic equations on time scales, Comput. math. Appl. 49, 1327-1334 (2005) · Zbl 1093.34023 · doi:10.1016/j.camwa.2005.01.016
[7]Dacunha, J. J.: Stability for time varying linear dynamic systems on time scales, J. comput. Appl. math. 176, 381-410 (2005) · Zbl 1064.39005 · doi:10.1016/j.cam.2004.07.026
[8]Kaymakcalan, B.: Lyapunov stability theory for dynamic systems on time scales, J. appl. Math. stochastic anal. 5, 275-281 (1992) · Zbl 0762.34027 · doi:10.1155/S1048953392000224
[9]Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[10]Lakshmikantham, V.; Vatsala, A. S.: Hybrid systems on time scales, J. comput. Appl. math. 141, 227-235 (2002) · Zbl 1032.34050 · doi:10.1016/S0377-0427(01)00448-4
[11]Yang, T.: Impulsive systems and control: theory and applications, (2001)
[12]Zhang, Y.; Sun, J.: Eventual practical stability of impulsive differential equations with time delay in terms of two measurements, J. comput. Appl. math. 176, 223-229 (2005) · Zbl 1063.34070 · doi:10.1016/j.cam.2004.07.014