Wirtinger-like Lyapunov-Krasovskii functionals for discrete-time delay systems

Time-dependent Lyapunov functionals appeared to be very efficient for sampled-data systems. Recently, new Lyapunov functionals were constructed for sampled-data control in the presence of a constant input delay. The construction of these functionals was based on Wirtinger's inequality leading to simplified and efficient stability conditions in terms of linear matrix inequalities. In this article, we extend the latter results to the discrete-time sampled-data systems.We showthat the proposed approach is less conservative on some examples with a lower number of decision variables.