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

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.