Question

The system y(t) = 15e^x(t) is ___________

(a) Stable with input x(t)

(b) Stable with output y(t)

(c) Stable with both input x(t) as well as output y(t)

(d) Not stable

I had been asked this question by my school principal while I was bunking the class.

Enquiry is from Characterization and Nature of Systems in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Correct answer is (c) Stable with both input x(t) as well as output y(t)

The explanation is: Given that y (t) = 15 e^x(t)

Let x (t) = u (t), that is bounded input

∴ y(t) = e^u(t),  that is bounded output

The bounded input produces bounded output hence system is stable with both input x (t) as well as output y (t).