A bridge between Lyapunov-Krasovskii and spectral approaches for stability of difference equations

In this paper, we analyze the stability properties of a class of systems governed by linear difference equations. Lyapunov stability and asymptotic stability are analyzed using two different approaches, namely Lyapunov-Krasovskii techniques and spectral techniques. In the case of commensurable delays, we carry out an analytical form of the solution, allowing us to determine necessary and sufficient conditions for stability. A link with discrete-time systems is made, and some comments on time-varying delays are proposed.***Copyright©2013 IFAC