Time-delayed impulsive control for a class of dynamical systems

For the impulsive control method, time delay is inevitable at the impulse instances. The stability for a class of dynamical systems with time-delayed impulses is investigated. A sufficient condition is obtained to guarantee their origins to be globally asymptotically stable, this condition reflects the relationship between the system parameters, impulse intervals and time delays. By using the derived results, the synchronization of these systems is also realized. Finally, take the classical Chua circuit and Chen chaotic system as examples, some numerical simulations are respectively given to demonstrate the effectiveness of the theoretical results.