Open Access
Translator Disclaimer
2013 Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales
Kexue Zhang, Xinzhi Liu
J. Appl. Math. 2013(SI25): 1-12 (2013). DOI: 10.1155/2013/313029


We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results.


Download Citation

Kexue Zhang. Xinzhi Liu. "Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales." J. Appl. Math. 2013 (SI25) 1 - 12, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1263.93177
MathSciNet: MR3032254
Digital Object Identifier: 10.1155/2013/313029

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI25 • 2013
Back to Top