If we want to define this system, we can say that the systems, which are not linear are non-linear systems. Clearly, all the conditions, which are being violated in the linear systems, should be satisfied in this case.

Conditions

• The output should not be zero when input applied is zero.

• Any non-linear operator can be applied on the either input or on the output to make the system non-linear.

Examples

To find out whether the given systems are linear or non-linear.

a) $y(t) = e^{x(t)}$

In the above system, the first condition is satisfied because if we make the input zero, the output is 1. In addition, exponential non-linear operator is applied to the input. Clearly, it is a case of Non-Linear system.

b) $y(t) = x(t+1)+x(t-1)$

The above type of system deals with both past and future values. However, if we will make its input zero, then none of its values exists. Therefore, we can say if the input is zero, then the time scaled and time shifted version of input will also be zero, which violates our first condition. Again, there is no non-linear operator present. Therefore, second condition is also violated. Clearly, this system is not a non-linear system; rather it is a linear system.