Asymptotic estimates and exponential stability for higher-order monotone difference equations
© Hindawi Publishing Corporation 2005
Received: 21 May 2004
Published: 14 March 2005
Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.