What is a characteristic of a system with poles located in the right half of the s-plane?

• A. The system is stable
• B. The system is unstable
• C. The system is oscillatory
• D. The system is overdamped

Answer: (B)

A system with poles located in the right half of the s-plane is characterized as unstable. In the context of control systems and signal processing, the poles of a system's transfer function dictate its behavior over time. When poles are in the right half of the s-plane, it means the corresponding time-domain solution involves exponentially increasing terms, resulting in output responses that diverge over time rather than converging to a steady state. This leads to an unstable system where outputs grow without bound in response to a bounded input.

The nature of the poles serves as an important indicator of stability. Poles that are located on the left half of the s-plane suggest stability, while those in the right half indicate instability. An oscillatory system can be linked to poles on the imaginary axis or pairs of complex conjugates with zero real parts, rather than those purely in the right half. Additionally, the terms overdamped, underdamped, and critically damped primarily pertain to systems with poles on the left half of the plane, specifically how they return to equilibrium. Thus, the correct characterization of a system with right half s-plane poles is instability.