Two-Sided Time-Domain Moment Matching for Linear Systems

Model Reduction by Moment Matching: Beyond Linearity A Review of the Last 10 Years

“…Remark 6. The matrices W and V contain the moments of the system ( 40)-( 41) at the eigenvalues of Λ and M if the following conditions hold: (Λ, R) is observable, (M, L) is reachable, R has a right inverse, and L has a left inverse [35].…”

Derivative-Extended Time Domain Reduction for Coupled Systems Using Chebyshev Expansion

“…The th Chebyshev approximation to the system output ( ) can be obtained directly from (8). There holds ( ) ≈ Discrete Dynamics in Nature and Society coefficients of ( ) are referred to as = T for = 0, 1, .…”

“…In Algorithm 4, one can calculate the vector by solving the first linear equation of (9) with much less effort, instead of solving the whole linear system directly. Once the vector is found, the matrices and with orthogonal columns can be obtained by using the well-known Arnoldi algorithm [8]. preserving Chebyshev coefficients of the derivatives.…”

“…By taking Laplace transformation, moment matching methods aim to provide a Páde-type approximation to the transfer function of original systems in the frequency domain. As the approximation can be achieved implicitly by Krylov-based projection methods, this kind of methods is computationally efficient and applies to extremely large scale systems [6][7][8][9]. However, reduced models resulting from this method may be unstable.…”

Nonlinear Model Reduction in the Loewner Framework

“…In [28] a data-driven model reduction approach using the Loewner framework is given for linear systems, where frequencyresponse data are inferred from trajectories of the input and output signals. Note that as a result of the definitions of moments in the time-domain in [3], it has been shown in [5] that the Loewner framework in [24] can be considered as a special case of a two-sided moment-matching procedure [29]. The Loewner framework has been developed for bilinear, quadratic-bilinear, and linear switched systems using a higherorder transfer function (frequency domain) approach in [30], [31], [32] respectively.…”