A pole located in the right-half of the s-plane implies the system is

• A. Stable
• B. Marginally stable
• C. Unstable with compensation required
• D. Unstable

Answer: (D)

The main idea is that stability for a continuous-time system hinges on where its poles sit in the s-plane. Poles with positive real parts cause terms that grow like e^{Re(s)t}, leading to an unbounded response over time. A pole in the right-half plane means the system's response increases without bound, so the system is unstable. The other options describe stable or marginal cases only if all poles are in the left half-plane (stable) or on the imaginary axis without growth (marginal stability); the presence of a right-half-plane pole overrides those, marking the system as unstable. Although compensation can be used to move poles into the left half-plane, the current system with a right-half-plane pole is simply unstable.