Advances in Difference Equations
Volume 2008 (2008), Article ID 598964, 15 pages
doi:10.1155/2008/598964
Uniform asymptotic stability and robust stability for positive linear Volterra difference equations in Banach lattices
Satoru Murakami1
and Yutaka Nagabuchi2
1Department of Applied Mathematics, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan
2Department of Applied Science, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan
Abstract
For positive linear Volterra difference equations in Banach lattices, the uniform asymptotic stability of the zero solution is studied in connection with the summability of the fundamental solution and the invertibility of the characteristic operator associated with the equations. Moreover, the robust stability is discussed and some stability radii are given explicitly.