Question

When are LTI systems stable?

(a) Only when bounded input produces a bounded output

(b) Only when bounded input produces a unbounded output

(c) Only when unbounded input produces a bounded output

(d) Only when unbounded input produces an unbounded output

I have been asked this question in an interview for job.

This interesting question is from Properties of LTI Systems in chapter Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

The correct choice is (a) Only when bounded input produces a bounded output

The explanation is: It follows from previous BIBO stability factor. It is the same for an LTI system too. Hence, a continuous or discrete time LTI system is said to be stable only when bounded input produces a bounded output.