Impulsive control and synchronization for a class of chaotic delayed systems

The issues of impulsive control and synchronization for a class of chaotic delayed systems are investigated in this paper. By establishing a generalized delayed Halanay differential inequality on impulsive dynamical systems, some simple yet generic criteria to guarantee impulsive stabilization and synchronization are analytically derived. Compared with some existing works, the distinctive features of these criteria indicate two aspects: On the one hand, these criteria can be used to address global exponential stability rather than (uniform) asymptotical stability of the controlled systems. On the other hand, these criteria are valid for any time delays since the restrictive condition that the time delays are less than the length of all the impulsive intervals is actually removed here. It is shown that impulses play an important role in making the controlled system globally exponentially stable and synchronous. Furthermore, two numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.