According to LTI system stability conditions, what should happen if you stop providing input?

• A. The output should increase
• B. The output should settle back to zero
• C. The system should maintain its last value
• D. The system should oscillate at the resonant frequency

Answer: (B)

In the context of Linear Time-Invariant (LTI) systems, the stability condition refers to how a system behaves when it is no longer receiving input. For an LTI system to be considered stable, when the input is stopped, the output must eventually settle back to zero, provided that the system starts in a state that does not contain persistent energy.

If the system is stable, when input is removed, any transient responses will decay, allowing the system to reach a steady state where the output eventually diminishes to zero. This behavior is crucial in ensuring that the system does not produce sustained oscillations or drifts, which would indicate instability.

This contrasts with behaviors such as increasing output or maintaining the last value, which would happen in systems that are unstable or that exhibit characteristics of a non-convergent response. Oscillating at the resonant frequency would imply that the system is in an unstable state, leading to continuous fluctuations rather than settling to a steady state.

Thus, the correct answer reflects the essential characteristic of stability in LTI systems, where the output returns to zero when the input is ceased.