In the Laplace-domain representation of a system, the location of poles determines stability. If a pole has a negative real part, the system response is:

• A. Unstable
• B. Marginally stable
• C. Decaying with time (stable)
• D. Oscillatory without decay

Answer: (C)

A pole with a negative real part corresponds to a time-domain term that looks like e^{σt} e^{jωt} with σ < 0. The factor e^{σt} decays exponentially as time goes on, so the amplitude of that component dies out. The imaginary part e^{jωt} only causes oscillation at frequency ω, but its envelope shrinks because of the negative real part. So the overall response settles to zero over time, meaning the system is stable for that mode. If all poles have negative real parts, the entire system’s response decays and remains bounded for bounded inputs.