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Linear System

A system may have input and output. Suppose the system receive input X and it produces output Y.

Difference Equation Tutorial: Linear System

A system is called a linear system if the system satisfied two conditions:

System that receive a sum of two inputs will also produce output equal to the sum of the two inputs

Difference Equation Tutorial: Linear System

System that receive a constant multiplication of input will also produce output equal to the constant multiplication of the input

Difference Equation Tutorial: Linear System

We can summarize the two conditions of the linear system into a linear combination. Thus, a linear system is a system that produces output equal to the linear combination of the input

Difference Equation Tutorial: Linear System

Examples

The following are the examples of linear system

  • Difference Equation Tutorial: Linear System
  • Difference Equation Tutorial: Linear System

A system that is not linear is called a non-linear system. The output is not a linear combination of the input. The following are the example of non-linear system

  • Difference Equation Tutorial: Linear System
  • Difference Equation Tutorial: Linear System
  • Difference Equation Tutorial: Linear System (second term is not a linear combination of input Difference Equation Tutorial: Linear System or past input Difference Equation Tutorial: Linear System )
Go on to the next lesson to have better undertanding of the examples above

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Preferable reference for this tutorial is

Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\