# Nonlinear Systems- 2 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 principal separately to get a clear understanding of what they mean and the basic assumptions behind each

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Transcription: Linear Systems Theory Before we talk about nonlinear systems we need to first have a basic understand what a linear system is. Linear systems are defined by their adherence to what is called the superposition principles. There are just two superposition principles and they are called homogeneity and additively. 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. Another way of stating the additivity principle is that for all linear systems, the net response caused by two or more stimuli is the sum of the response which would have been caused by each stimulus individually. Our second superposition principle, homogeneity, states that the output to a linear system is always directly proportional to the input, so if we put twice…

- Kind: Short
- Year: 2015
- Runtime: 5 min
- By: Complexity Academy
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Nonlinear_Systems-_2_Linear_Systems_Theory.webm)
- Licence or status: [CC BY 3.0](https://creativecommons.org/licenses/by/3.0) (as the archive states it)
- Credit: Complexity Academy
- Who can watch: Tweens profiles and older (the archive gives no rating; placed by Invisible Network from its collection and subjects)

[Watch now](https://invisiblenetwork.ai/watch/archive/commons/58002295?play=1)