Year: 2023
Type: preprint
Abstract: The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of high-dimensional second-order dynamical systems, avoiding the first-order double-sized equivalent representation. The moments of a second-order system are characterized by the solutions of second-order Sylvester equations, leading to families of parameterized second-order reduced models that match the moments of the original system at selected interpolation points. A two-sided moment matching problem is also addressed, yielding a unique second-order reduced system that matches two distinct sets of interpolation points. Furthermore, we construct reduced second-order systems that match the moments of both the transfer function and its first-order derivative. Then, we also discuss how the proposed framework can be extended to multiple-input multiple-output (MIMO) second-order systems through tangential interpolation, and we identify the main open difficulties in extending the derivative-matching and pole-zero placement results to the MIMO setting. The theory is illustrated on a numerical example of vibrating systems.
Source: arXiv (Cornell University)
Authors: Cheng, Xiaodong, Ionescu, Tudor C.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Academia Româna
Award: G6372760959
OpenAlex ID: W4376864588