Definition check: what is a “stable system” in control engineering (BIBO stability)?

Introduction / Context: Stability is the bedrock of controller design. The most common and practically meaningful definition for linear time-invariant (LTI) systems is bounded-input bounded-output (BIBO) stability. If a plant or closed loop is not BIBO-stable, even small input disturbances can lead to runaway outputs and unsafe operation.

Given Data / Assumptions:

• We refer to continuous-time LTI systems under standard feedback.
• “Bounded” means the magnitude remains finite for all time.
• No special input class (sinusoid only, etc.) is assumed; any bounded input qualifies.

Concept / Approach: A system is BIBO-stable if every bounded input produces a bounded output. This is equivalent (for LTI systems) to having all closed-loop poles strictly in the left half of the complex plane. Other statements (e.g., “servo conditions” or selective input classes) are neither necessary nor sufficient as a general definition.

Step-by-Step Solution:

Verification / Alternative check: Nyquist and Routh–Hurwitz methods test whether all closed-loop poles lie in the left half-plane, ensuring BIBO stability and hence satisfying the definition.

Why Other Options Are Wrong:

Common Pitfalls: Confusing asymptotic stability with BIBO stability in nonlinear contexts; for LTI systems, BIBO and internal stability line up under standard conditions.

Final Answer: for which the output response is bounded for all bounded input