Impulsive control for stabilisation of discrete delay systems and synchronisation of discrete delay dynamical networks

Abstract

This study investigates impulsive stabilisation of non-linear discrete-time systems with time-delay. By employing Razumikhin technique and Lyapunov functions, several global exponential stability criteria are established. It is shown that, even if the non-linear discrete delay systems, in the absence of impulses, are unstable, impulses can exponentially stabilise the system with an estimated convergence rate. Moveover, these impulsive stabilisation results can be applied to design impulsive control scheme to achieve exponential synchronisation of discrete dynamical networks with coupling time-delays. Synchronisation criteria are obtained by using some simple forms of Lyapunov functions. Some numerical examples are given to illustrate the authors' results.