In this paper, we consider the Korteweg–de Vries equation with time-dependent delay on boundary or internal feedbacks. Under some assumptions delay, weights of feedbacks and length spatial domain, prove exponential stability results, using appropriate Lyapunov functionals. We finish by numerical simulations that illustrate results influence decay rate.

A convex approach is proposed to deal with switched discrete-time systems with time-varying delays. It uses a parameter dependent Lyapunov-Krasovskii functional that allows to assure the robust stability or the robust stabilization of a switched system for arbitrary switching functions. The analysis and the design conditions are formulated as simple feasibility tests of linear matrix inequaliti...