What is the sensitivity function and what does it tell us?

The sensitivity function S(s) = 1/(1 + G(s)H(s)) describes how the closed-loop transfer function changes with plant variations. Low |S| means the system is insensitive to plant changes and rejects disturbances well. Complementary sensitivity T(s) = G(s)H(s)/(1 + G(s)H(s)) is the closed-loop transfer function; S + T = 1. Design trade-off: reducing sensitivity at low frequencies (good tracking/rejection) increases it at high frequencies (noise amplification, robustness issues). Robust control designs with sensitivity bounds.