STABILITY PRESERVATION IN GALERKIN-TYPE PROJECTION-BASED MODEL ORDER REDUCTION

被引:5
作者
Pulch, Roland [1 ]
机构
[1] Univ Greifswald, Inst Math & Comp Sci, Walther Rathenau Str 47, D-17489 Greifswald, Germany
来源
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2019年 / 9卷 / 01期
关键词
dynamical system; ordinary differential equation; model order reduction; Galerkin projection; asymptotic stability; Lyapunov equation; alternating direction implicit method; BALANCED TRUNCATION;
D O I
10.3934/naco.2019003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may be unstable, even though the original system is asymptotically stable. We focus on projection-based model order reduction of Galerkin-type. A transformation of the original system guarantees an asymptotically stable reduced system. This transformation requires the numerical solution of a high-dimensional Lyapunov equation. We specify an approximation of the solution, which allows for an efficient iterative treatment of the Lyapunov equation under a certain assumption. Furthermore, we generalize this strategy to preserve the asymptotic stability of stationary solutions in model order reduction of nonlinear dynamical systems. Numerical results for high-dimensional examples confirm the computational feasibility of the stability-preserving approach.
引用
收藏
页码:23 / 44
页数:22
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