According to classical control theory, a system is stable when its transfer function poles are located:

• A. On the imaginary axis
• B. In the right half of the s-plane
• C. In the left half of the s-plane
• D. At the origin only

Answer: (C)

A system is considered stable in classical control theory when all of its transfer function poles are located in the left half of the s-plane. This is because poles in this region correspond to exponentially decaying response behavior over time, indicating that any disturbances or initial conditions will die out, allowing the system to return to equilibrium.

In contrast, poles located on the imaginary axis would suggest a system that oscillates indefinitely, leading to marginal stability. Poles in the right half of the s-plane result in exponentially growing responses, which indicate an unstable system that moves further away from equilibrium over time. Poles fixed solely at the origin imply constant gain without attenuation or growth, reflecting a special case rather than providing stability criteria. Thus, the clear criterion for stability remains the position of poles exclusively in the left half of the s-plane.