The Black Box Approach and Systems with Memory

Abstract

Any kind of approach to the description of a real system has some inherent advantages over other kinds in the wealth of conclusions and the easiness of their deduction, as well in what it does or does not come natural to say about the studied system. This lecture is meant as a short sight—seeing tour intended to convey an idea of what the black—box approach is all about.

Suppose we have a collection of identical systems, say T, which we are observing during the time interval t ∈ [0,∞) from the outside. We notice that our inputs. say i_in = i_in(t), t ∈ [0,∞), to T are transformed into uniquely determined outputs, say i_out = i_out,(t), t E [0,∞) a fact we choose to represent as follows:

$$ {\text{i}}_{{\text{out}}} = {\text{A}}\left\{ {{\text{i}}_{{\text{in}}} } \right\} + {\text{q,}}\,\,\,\,\,{\text{A}}\left\{ 0 \right\} = 0. $$

(1.1)