Which statement about BIBO stability is true?

Which statement about BIBO stability is true?

• A. It requires zero input for stability
• B. It ensures outputs are always bounded regardless of input
• C. It requires unbounded inputs to test stability
• D. It yields bounded outputs for every bounded input

Answer: (D)

Bounded-input, bounded-output stability means that if you feed the system any signal of finite magnitude, the response stays finite. The statement that outputs are bounded for every bounded input matches this definition exactly, since it directly ties the system’s behavior to inputs with finite amplitude. It doesn’t require the input to be zero, and it doesn’t say anything about unbounded inputs or guarantee stability under them. The other options misstate the concept: one focuses on zero input, another suggests outputs stay bounded for all inputs regardless of size (including unbounded ones), and another implies testing with unbounded inputs.

Bounded-input, bounded-output stability means that if you feed the system any signal of finite magnitude, the response stays finite. The statement that outputs are bounded for every bounded input matches this definition exactly, since it directly ties the system’s behavior to inputs with finite amplitude. It doesn’t require the input to be zero, and it doesn’t say anything about unbounded inputs or guarantee stability under them. The other options misstate the concept: one focuses on zero input, another suggests outputs stay bounded for all inputs regardless of size (including unbounded ones), and another implies testing with unbounded inputs.