Stabilization of nonlinear time-delay systems: Flexible delayed impulsive control

This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. Some sufficient conditions are provided for establishing stability property in terms of exponential Lyapunov-Razumikhin functions. It is shown that the size of delay in continuous dynamics can be flexible. Specially, it can be smaller or larger than the impulsive intervals, and there is no magnitude relationship between the delay in continuous flow and impulsive delay. In most existing results, from the impulsive control point of view, the Lyapunov functions were based on the assumption that there was a common threshold at every impulse point. In this study, utilizing the proposed method of average impulsive estimation (AIE), the rate coefficients are flexible, and the impulsive delay can be integrated to guarantee the effect of stabilization of impulses. As an application, the theoretical results are applied to the synchronization of a chaotic neural network, and the impulsive control input is formalized in terms of linear matrix inequalities (LMIs). The efficiency of the derived results is illustrated by two numerical examples.