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...

}(x)} are real-valued, the Bessel functions of the first and second kind are the real and imaginary parts, respectively, of the first Hankel function and...

introducing the Hankel transform and the Hankel matrix. Hankel was born on 14 February 1839 in Halle, Germany. His father, Wilhelm Gottlieb Hankel, was a physicist...

underlying state-space or hidden Markov model is desired. The singular value decomposition of the Hankel matrix provides a means of computing the A, B, and C matrices...

Coefficient diagram method Control reconfiguration Feedback H infinity Hankel singular value Krener's theorem Lead-lag compensator Minor loop feedback Multi-loop...

Barkhausen stability criterion Circle criterion Control engineering Hankel singular value Reinschke, Kurt (2014). "Chapter 4.3. Das Stabilitätskriterium von...

systems Fractional-order control Fuzzy logic H-infinity loop-shaping Hankel singular value Kalman filter Krener's theorem Least squares Lyapunov stability...

Coefficient diagram method Control reconfiguration Feedback H infinity Hankel singular value Krener's theorem Lead-lag compensator Markov chain approximation...

meaningful interpretation. The name "singular spectrum analysis" relates to the spectrum of eigenvalues in a singular value decomposition of a covariance matrix...

Controllability Observability Gramian Gramian matrix Minimum energy control Hankel singular value Chen, Chi-Tsong (1999). Linear System Theory and Design Third Edition...

found in. Observability Controllability Gramian Gramian matrix Hankel singular value Chen, Chi-Tsong (1999). Linear System Theory and Design Third Edition...

decomposition Reducing subspace Spectral theorem Singular value decomposition Higher-order singular value decomposition Schur decomposition Schur complement...

{\displaystyle B=JC^{T}\,} then the absolute value of the eigenvalues of the cross Gramian equal Hankel singular values: | λ ( W X ) | = λ ( W C W O ) . {\displaystyle...

approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to numerous other techniques...

integration is done over the Hankel contour H, is valid for all complex s not equal to 1. Residue (complex analysis) Cauchy principal value Poisson integral Pochhammer...

operator interpolation spaces, singular integrals and Besov spaces, differential geometry, Clifford analysis, Fock space and Hankel operators, Fourier and harmonic...

direction coefficient, often used for cos φ + i sin φ, is due to Hankel (1867), and absolute value, for modulus, is due to Weierstrass. Later classical writers...

which led to the result bearing his name. It was first published by Hermann Hankel in 1861. This classical case relates the surface integral of the curl of...

Hankel function and K1 is a modified Bessel function. This expression can be derived directly from the field theory as the vacuum expectation value of...

in 1985 with a Ph.D. His Ph.D. thesis, dealing with geometric aspects of Hankel operators and Toeplitz operators, was supervised by Nikolai Kapitonovich...

Centrosymmetric matrix Circulant matrix Covariance matrix Coxeter matrix GCD matrix Hankel matrix Hilbert matrix Persymmetric matrix Sylvester's law of inertia Toeplitz...

of the latter. The polylogarithm may be quite generally represented by a Hankel contour integral (Whittaker & Watson 1927, § 12.22, § 13.13), which extends...

two of the three regular singularities merge into an irregular singularity. The term confluent refers to the merging of singular points of families of differential...

(2002), Operators, functions, and systems: an easy reading, Vol. 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, vol. 92, American Mathematical...

rejects this definition because it doesn't fix the truth value of identity statements when a singular term not of the form 'the number of Fs' flanks the identity...

_{H}{\frac {(-x)^{s-1}}{e^{x}-1}}\,\mathrm {d} x} for all s (where H denotes the Hankel contour). We can also find expressions which relate to prime numbers and...

for the Fourier transform of a radial function. This is essentially the Hankel transform. Moreover, there is a simple recursion relating the cases n +...

and vibration before studying the ERA. Given pulse response data form the Hankel matrix H ( k − 1 ) = [ Y ( k ) Y ( k + 1 ) ⋯ Y ( k + p ) Y ( k + 1 ) ⋱ ⋮...

another G-function, and generalizations of integral transforms like the Hankel transform and the Laplace transform and their inverses result when suitable...

Arithmetic-Geometric Mean of Gauss by David A. Cox. Milne, Steven C. (2000). "Hankel Determinants of Eisenstein Series". arXiv:math/0009130v3. The paper uses...