Model reduction of bilinear systems described by input–output difference equation

Abstract

A class of single input single output bilinear systems described by their input-output difference equation is considered. A simple expression for the Volterra kernels of the system is derived in terms of the coefficients of difference equation. An algorithm, based on the singular value decomposition of a generalized Hankel matrix, is also developed. The algorithm is then used to find a reduced-order bilinear state-space model. The Hankel approach will be extensively studied under different data length cases and different orders of the state-space models. A numerical example is presented to illustrate the effectiveness of the proposed algorithm.

Interpolation-Based ${\cal H}_2$-Model Reduction of Bilinear Control Systems

“…with dimensions as defined in (1) and transfer function H (s) = C (sI n − A ) −1 B . So far, we did not further specify criteria which allow to measure the quality of a reducedorder system.…”

“…N k x(t)u k (t) + Bu(t), y(t) = Cx(t), x(0) = x 0 , (1) with A, N k ∈ R n×n , B ∈ R n×m , C ∈ R p×n , u(t) = u 1 (t) . .…”

Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems

“…An interesting feature of this special class of nonlinear systems now is their close relationship to linear systems which allows generalising some of the concepts from the linear case, see e.g. Al-Baiyat (2004). Formally, throughout this article, our goal will be the construction of a reduced-order system b AE :x ðk þ 1Þ ¼ÂxðkÞ þN I m xðkÞ ð Þ uðkÞ þBuðkÞ, yðkÞ ¼ĈxðkÞ,xð0Þ ¼x 0 , ( ð2Þ with 2 Rn Ân ,N ¼ ½N 1 , .…”