Exponential stability of slowly varying discrete systems with multiple state delays

Abstract

SUMMARYWe give sufficient conditions for the exponential stability of a class of perturbed time‐varying difference equations with multiple delays and slowly varying coefficients. Under appropriate growth conditions on the perturbations, combined with the ‘freezing’ technique, we establish explicit conditions for global exponential stability. Copyright © 2012 John Wiley & Sons, Ltd.

WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems

“…Recently, by associating the second Lyapunov method and the Lyapunov matrix equation approach, sufficient conditions for exponential stability and explicit exponential estimates of solutions of system are derived in , which generalizes the result obtained in . Furthermore, the results obtained in were extended to the perturbed LDDSs in , and to the time‐varying LDDSs in .…”