METRIC COMPLEXITY OF CAUSAL LINEAR-SYSTEMS - EPSILON-ENTROPY AND EPSILON-DIMENSION FOR CONTINUOUS TIME

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 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. Copyright © 1979 by The Institute of Electrical and Electronics Engineers Inc.