Synchronization issue of uncertain time-delay systems based on flexible impulsive control

This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the $\varpi (t)$, which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method is introduced through using the variable impulsive gain and time-varying delays. It is interesting to find that uncertain time-delay systems can maintain GES by adjusting the impulsive gain and impulsive delay. Finally, two simulations are given to illustrate the effectiveness of the derived results.