Difference equations in continuous time with distributed delay: Exponential estimates

In this paper, we propose new sufficient conditions for the exponential stability of a class of systems governed by continuous-time difference equations with distributed delay. These conditions are obtained by the Lyapunov-Krasovskii approach, and come down to solve tractable linear matrix inequalities which are delay dependent. These conditions provide also a direct estimation of the exponential decay rate of the system response. Improvements on the conservatism in the proposed condition are discussed with respect to previous conditions which appeared in the literature.