  Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.
