GATE EE 2024 Set 1 — Question 38
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Question
Consider the discrete-time systems and defined as follows:Which one of the following statements is true?
Correct answer
(D) T₁ is not BIBO stable but T₂ is BIBO stable.
Solution
A system is Bounded-Input Bounded-Output (BIBO) stable if every bounded input produces a bounded output.
1.For : Let the input be a unit step , which is bounded (). The output is:
As , . Since a bounded input produces an unbounded output, is not BIBO stable.2.For : Let the input be bounded such that for all . The output is:
As , the geometric series converges:Since the output is bounded by for any bounded input, is BIBO stable.Continue learning with Success Tracker
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