On the metric complexity of causal linear systems: Estimates of ε-entropy and ε-dimension

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)| < Ce^-at, and frequency responses satisfy an attenuation condition |F(jω)|< Kω^-1. The dependance of ε-entropy and ε-dimension on the accuracy ε is characterized by order, type, and power indeces. Similar results for the discrete-time case are reviewed and compared.