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 show that the proposed approach is less conservative on some examples with a lower number of decision variables.