Question

The system characterized by the equation y(t) = ax(t) + b is

(a) Linear for any value of b

(b) Linear if b > 0

(c) Linear if b < 0

(d) Non-linear

This question was addressed to me by my college director while I was bunking the class.

This question is from The z- and s-Domain Relationship in section Digital Control Systems of Control Systems

Answer 1

Right choice is (d) Non-linear

The explanation: The system is non-linear because x(t) = 0 does not lead to y (t) = 0, which is a violation of the principle of homogeneity.