Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

Abstract

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

“…Therefore, model order reduction becomes important and popular. So far, many effective methods have emerged to reduce the large-scale linear time invariant (LTI) models, such as Krylov subspace method (Grimme, 1997; Yuan et al, 2018), balanced truncation method (Haider et al, 2017; Yang and Jiang, 2020; Zhou et al, 2001), orthogonal decomposition method (Yuan et al, 2018), optimal model order reduction method (Jiang and Xu, 2017; Sato and Sato, 2017; Vasu et al, 2018), and so on.…”