In control theory, **Hankel singular values**, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for balanced model reduction, in which high energy states are retained while low energy states are discarded. The reduced model retains the important features of the original model.

Hankel singular values are calculated as the square roots, {σ_{i} ≥ 0, *i* = 1,…,*n*}, of the eigenvalues, {λ_{i} ≥ 0, *i* = 1,…,*n*}, for the product of the controllability Gramian, *W*_{C}, and the observability Gramian, *W*_{O}.