GATE EE 2015 Set 2 — Question 54
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Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
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Question
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?
Correct answer
(D) The unit step response will be bounded.
Solution
By definition, a system is Bounded Input Bounded Output (BIBO) stable if every bounded input results in a bounded output.
- The necessary and sufficient condition for an LTI system to be BIBO stable is that its impulse response must be absolutely integrable: . Thus, (A) is false.
- Finite support is not required for stability; many stable systems have infinite-duration impulse responses (e.g., ). Thus, (B) is false.
- For a stable system, the unit step response typically approaches a non-zero constant as , which is not absolutely integrable over . Thus, (C) is false.
- Since the unit step is a bounded input (), the corresponding output (the unit step response) must be bounded for a BIBO stable system. Thus, (D) is true.
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