Krylov subspace-based model reduction for a class of bilinear descriptor systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:315

Article

Ahmad, Mian Ilyas¹  Benner, Peter¹  Goyal, Pawan¹ 

[1] Max Planck Inst Dynam Complex Tech Syst, Sandtorstr 1, D-39016 Magdeburg, Germany

关键词: Krylov subspace;    Bilinear systems;    Descriptor systems;    Model order reduction;    Moment-matching;    Transfer functions;   

DOI  :  10.1016/j.cam.2016.11.009

来源: Elsevier

【 摘 要 】

We consider model order reduction for bilinear descriptor systems using an interpolatory projection framework. Such nonlinear descriptor systems can be represented by a series of generalized linear descriptor systems (also called subsystems) by utilizing the Volterra-Wiener approach (Rugh, 1981). Standard pro\jection techniques for bilinear systems utilize the generalized transfer functions of these subsystems to construct an interpolating approximation. However, the resulting reduced-order system may not match the polynomial parts of the generalized transfer functions. This may result in an unbounded error in terms of H-2 or H-infinity norms. In this paper, we derive an explicit expression for the polynomial part of each subsystem by assuming a special structure of the bilinear system which reduces to an index-1 linear descriptor system or differential algebraic equation (DAE) if the bilinear terms are zero. This allows us to propose an interpolatory technique for bilinear DAEs which not only achieves interpolation, but also retains the polynomial parts of the bilinear systems. The approach extends the interpolatory technique for index-1 linear DAEs (Beattie and Gugercin, 2009) to bilinear DAEs. Numerical examples are used to illustrate the theoretical results. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free