Hankel singular value

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, "WC", and the observability Gramian, "WO".

ee also

*Hankel matrix
*Hermann Hankel

External links

*cite journal|last = Kenney|first = C.|coauthors = Hewer, G.|title = Necessary and sufficient conditions for balancing unstable systems|journal = IEEE Transactions on Automatic Control|volume = 32|issue = 2|date = Feb 1987|url = http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1104553


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Hankel matrix — In linear algebra, a Hankel matrix, named after Hermann Hankel, is a square matrix with constant (positive sloping) skew diagonals, e.g.::egin{bmatrix}a b c d e b c d e f c d e f g d e f g h e f g h i end{bmatrix}.In mathematical terms::a {i,j} …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • Control theory — For control theory in psychology and sociology, see control theory (sociology) and Perceptual Control Theory. The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is… …   Wikipedia

  • Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

  • List of linear algebra topics — This is a list of linear algebra topics. See also list of matrices glossary of tensor theory. Contents 1 Linear equations 2 Matrices 3 Matrix decompositions 4 …   Wikipedia

  • Propagator — This article is about Quantum field theory. For plant propagation, see Plant propagation. Quantum field theory …   Wikipedia

  • Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… …   Wikipedia

  • Diophantus — For the general, see Diophantus (general). Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. Diophantus of Alexandria (Greek: Διόφαντος ὁ Ἀλεξανδρεύς XD. b. between 200 and 214… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”