Question

When we take up design of systems, ideally how do we define the stability of a system?

(a) A system is stable, if a bounded input gives a bounded output, for some values of the input

(b) A system is unstable, if a bounded input gives a bounded output, for all values of the input

(c) A system is stable, if a bounded input gives a bounded output, for all values of the input

(d) A system is unstable, if a bounded input gives a bounded output, for some values of the input

The question was posed to me by my school teacher while I was bunking the class.

The question is from System Classification and Properties topic in portion Signals and Systems Basics of Signals and Systems

Answer 1

Correct answer is (c) A system is stable, if a bounded input gives a bounded output, for all values of the input

The explanation is: For designing a system, it should be kept in mind that the system does not blow out for a finite input. Thus, every finite input should give a finite output.