Question

The system is stable when y(t)= tx(y).

(a) True

(b) False

The question was asked in homework.

This key question is from BIBO Stability & Systems in the Time Domain topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Right choice is (b) False

Easiest explanation: Here we can see,

|x(t)|≤Bx<∞,  for all t.

Using the input output relation we have y(t)= tx(y). And so we may write, |Y(t)|=|tx(t)|=|t||x(t)|=|t|Bx.

As tends to infinity, the output also tends to infinity.  That is it is unbounded.  So it is unstable.