What does a positive pole in a transfer function indicate?

In control systems and signal processing, a positive pole in the transfer function is indicative of an unstable system. The poles of a transfer function are the values of s (complex frequency) that cause the denominator to equal zero, leading to a system response that can become unbounded over time.

When a pole is located in the right half of the s-plane (which corresponds to a positive real part), it signifies that the system's output will grow exponentially over time rather than stabilize at a steady state. This behavior results in the output not returning to equilibrium, which is a hallmark of instability. Additionally, in terms of system response, the presence of a positive pole means that any disturbance or input will lead to an increasing output response, reflecting a lack of control over the system’s dynamics.

Understanding this concept is crucial for engineers working with feedback control systems, as stability is a key requirement in many applications; knowing that a positive pole points towards instability allows for necessary adjustments in system design and control strategies to ensure desired performance and safety.