  The class of controlled synchronization systems under information constraints
imposed by limited information capacity of the coupling channel is analyzed. It
is shown that the framework proposed in A. L. Fradkov, B. Andrievsky, R. J.
Evans, Physical Review E 73, 066209 (2006) is suitable not only for
observer-based synchronization but also for controlled master-slave
synchronization via communication channel with limited information capacity. A
simple first order coder-decoder scheme is proposed and a theoretical analysis
for multi-dimensional master-slave systems represented in the Lurie form
(linear part plus nonlinearity depending only on measurable outputs) is
provided. An output feedback control law is proposed based on the Passification
theorem. It is shown that the upper bound of the limit synchronization error is
proportional to the upper bound of the transmission error. As a consequence,
both upper and lower bounds of limit synchronization error are proportional to
the maximum rate of the coupling signal and inversely proportional to the
information transmission rate (channel capacity). The results are applied to
controlled synchronization of two chaotic Chua systems coupled via a controller
and a channel with limited capacity.
