Linear Systems Theory

In this lecture we will discuss linear systems theory which is based upon the superposition principles of additivity and homogeneity, we will explore both of these principals separately to get a clear understanding of what they mean and the basic assumptions behind each. Firstly additively, which states that we can add the effect or output of two systems together and the resulting combined system will be nothing more that the simple addition of each system’s output in isolation. So for example, if I have two horses that can each pull a hundred kilograms of weight on a cart in isolation, well if I then combine these two horses to tow a single larger cart they will be able to pull twice as much weight. Secondly, the superposition principle, homogeneity, states that the output to a linear system is always directly proportional to the input, so if we put twice as much into the system we will in turn get out twice as much.