  We define the complexity of a continuous-time linear system to be the minimum
number of bits required to describe its forward increments to a desired level
of fidelity, and compute this quantity using the rate distortion function of a
Gaussian source of uncertainty in those increments. The complexity of a linear
system has relevance in control-communications contexts requiring local and
dynamic decision-making based on sampled data representations. We relate this
notion of complexity to the design of attention-varying controllers, and
demonstrate a novel methodology for constructing source codes via the endpoint
maps of so-called emulating systems, with potential for non-parametric,
data-based simulation and analysis of unknown dynamical systems.
