Observer (estimator): ẋ̂ = A x̂ + B u + L (y - ŷ), ŷ = C x̂. The correction term L(y - Cx̂) drives the estimate toward the true state.
Observer error dynamics: ė = (A - LC) e, where e = x - x̂. The observer poles are eigenvalues of A - LC.
Separation principle: The closed-loop poles of observer-based state feedback are the union of controller poles (A-BK) and observer poles (A-LC). Design them independently!
Bandwidth tradeoff: Faster observer (larger bandwidth) → quicker convergence but amplifies sensor noise. Slower observer → smoother estimates but lag behind true state.