Modified impulsive synchronization of hyperchaotic systems

In an original impulsive synchronization only instantaneous errors are used to determine the impulsive inputs. To improve the synchronization performance, addition of an integral term of the errors is proposed here. In comparison with the original form, the proposed modification increases the impulse distances which leads to reduction in the control cost as the most important characteristic of the impulsive synchronization technique. It can also decrease the error magnitude in the presence of noise. Sufficient conditions are presented through four theorems for different situations (nominal, uncertain, noisy, and noisy uncertain cases) under which stability of the error dynamics is guaranteed. Results from computer based simulations are provided to illustrate feasibility and effectiveness of the modified impulsive synchronization method applied on Rossler hyperchaotic systems.