Control systems can be represented with a set of mathematical equations known as mathematical model.

Mathematical models are useful for analysis and design of control systems. Analysis of control system means finding the output when we know the input and mathematical model. On the other hand, 'Design of control system' means finding the mathematical model when we know the input and the output. Mathematical models can take many different forms, and thus it is not an easy task to classify all the mathematical models.

The following mathematical models are mostly used:

(i) Differential equation model

(ii) Transfer function model

(iii) State space model

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