  Impulsively synchronized chaos with criterion from conditional Lyapunov
exponent is often interrupted by desynchronized bursts. This is because the
Lyapunov exponent cannot characterize local instability of synchronized
attractor. To predict the possibility of the local instability, we introduce a
concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum
of local Lyapunov exponents over the attractor. The SLLE is independent of the
system trajectories and therefore, can characterize the extreme expansion
behavior in all local regions with prescribed finite-time interval. It is shown
that the impulsively synchronized chaos can be kept forever if the largest SLLE
of error dynamical systems is negative and then the burst behavior will not
appear. In addition, the impulsive synchronization with negative SLLE allows
large synchronizable impulsive interval, which is significant for applications.
