A Novel Krylov Method for Model Order Reduction of Quadratic Bilinear Systems

2018 ◽  
Author(s):  
Xingang Cao ◽  
Joseph Maubach ◽  
Siep Weiland ◽  
Wil Schilders
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Bilinear Systems ◽  
Model Order ◽  
Krylov Method

scholarly journals Interpolatory model reduction for quadratic-bilinear systems using error estimators

2018 ◽  
Vol 36 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Mian Ilyas Ahmad ◽  
Peter Benner ◽  
Lihong Feng
Keyword(s):  
Model Reduction ◽  
Error Bound ◽  
Model Order Reduction ◽  
Computational Cost ◽  
Order Reduction ◽  
Bilinear Systems ◽  
Descriptor System ◽  
Model Order ◽  
Content Type ◽  
Projection Matrices

Purpose The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system. Design/methodology/approach The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework. Findings The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time). Originality/value In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

A Note on Projection Techniques for Model Order Reduction of Bilinear Systems

2007 ◽  
Author(s):  
Lihong Feng ◽  
Peter Benner ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Bilinear Systems ◽  
Model Order ◽  
Projection Techniques
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