Journal of Applied Mathematics
Volume 2013 (2013), Article ID 313029, 12 pages
http://dx.doi.org/10.1155/2013/313029
Research Article

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

Kexue Zhang1 and Xinzhi Liu2

1School of Control Science and Engineering, Shandong University, Jinan 250061, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 18 November 2012; Accepted 7 January 2013

Academic Editor: Qiru Wang

Copyright © 2013 Kexue Zhang and Xinzhi Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.