On the exponential stability of dynamic equations on time scales

In this paper, we deal with some theorems on the exponential stability of trivial solution of time-varying non-regressive dynamic equation on time scales with bounded graininess. In particular, well-known Perron’s theorem is generalized on time scales. Under rather restrictive condition, that is, integral boundedness of coefficient operators, we obtain a characterization of the uniformly exponential stability. © 2006 Elsevier Inc. All rights reserved