Hankel singular value

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.

See also

• Hankel matrix
• Hermann Hankel

External links

• Kenney, C.; Hewer, G. (Feb 1987). "Necessary and sufficient conditions for balancing unstable systems". IEEE Transactions on Automatic Control. 32 (2): 157. doi:10.1109/TAC.1987.1104553. 

Further reading

• Antoulas, Athanasios C. (2005). Approximation of Large-Scale Dynamical Systems. SIAM. ISBN 978-0-89871-529-3. doi:10.1137/1.9780898718713.