On the metric complexity of casual linear systems: ε -Entropy and ε -Dimension for continuous time

Estimates of e-entropy and e-dimension in the Kolmogorov sense are obtained for a class of causal, linear, time-invariant, continuous-time systems under the assumptions that impulse responses, satisfy an exponential order condition |f(t)| \leq Ce ^{-at} , and frequency responses satisfy an attenuation condition |F(j\omega)|\leg K\omega^{-1} . The dependence of e-entropy and e-dimension on the accuracy e is characterized by order, type, and power indexes. Similar results for the discrete-time case are reviewed and compared.