Statement (I): Linear system may have multiple equilibrium states.

Statement (II): If a system is BIBO stable, it must also be zero-input or asymptotically stable.

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ESE Electronics Prelims 2021 Official Paper
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  1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

  2. Both Statement (I) and Statement (II) are individually true, but Statement (II) is not the correct explanation of Statement (I).
  3. Statement (I) is true, but Statement (II) is false.
  4. ​Statement (I) is false, but Statement (II) is true.

Answer (Detailed Solution Below)

Option 4 : ​Statement (I) is false, but Statement (II) is true.
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Detailed Solution

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If the system is linear time invariant, i.e.

if f(x, t) = AX

Then there exist only one equilibrium state if A is non-singular, and there exist infinitely equilibrium states if A is singular. BIBO stability implies Asymptotic stability.

​Statement (I) is false, but Statement (II) is true.

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