Advances in Difference Equations
Volume 2005 (2005), Issue 2, Pages 133-144
doi:10.1155/ADE.2005.133

Exponential stability of dynamic equations on time scales

Allan C. Peterson1 and Youssef N. Raffoul2

1Department of Mathematics, College of Arts and Sciences, University of Nebraska–Lincoln, Lincoln 68588-0130, NE, USA
2Department of Mathematics, College of Arts and Sciences, University of Dayton, Dayton 45469-2316, OH, USA

Received 6 July 2004; Revised 16 December 2004

Copyright © 2005 Hindawi Publishing Corporation. 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 the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given.