Introduction to System Science with MATLAB, 2nd Edition

3Basic System Equations

In this chapter, we will undertake the essential task of converting the principle of causality into a quantitative mathematical statement for systems with any number of inputs and outputs. We will develop this generalized, fundamental mathematical framework for both discrete and continuous systems and for systems with and without feedback.

3.1 Functional Dependence of System Causes and Effects

A primary objective of system analysis is the determination and evaluation of the relationship between the inputs or causes imposed on a system and the outputs or effects produced by the system because of these inputs. Knowledge and understanding of this relationship are valuable for several reasons. First, accurate knowledge of the relationship between cause and effect for a given system leads to some understanding of the behavior and inner operations or internal mechanics of that system and is a vital step in fully understanding the operation and nature of the system. Second, with the cause and effect relationship adequately known, it is possible to explain the past performance of the system and to predict the output or response of the system for any permissible future input. Third, with the output response of the system known for any input, it is then possible to develop means for controlling or influencing the system in some desirable or optimal manner.

If a complete and accurate relationship between the system output response and any possible input is known ...