On the metric complexity of casual linear systems: ε -Entropy and ε -Dimension for continuous time
G. Zames · IEEE Transactions on Automatic Control · 1979
Estimates of ε-entropy and ε-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 ε-entropy and ε-dimension on the accuracy ε is characterized by order, type, and power indexes. Similar results for the discrete-time case are reviewed and compared.