A note on modeling some classes of nonlinear systems from data

We study the modeling of bilinear and quadratic systems from measured data. The measurements are given by samples of higher order frequency response functions. These values can be identified from the corresponding Volterra series of the underlying nonlinear system. We test the method for examples from structural dynamics and chemistry

Interpolatory Weighted-H2 Model Reduction

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach

Rational interpolation and state-variable realizations

AbstractThe problem is considered of passing from interpolation data for a real rational transfer-function matrix to a minimal state-variable realization of the transfer-function matrix. The tool is a Loewner matrix, which is a generalization of the Standard Hankel matrix of linear system realization theory, and which possesses a decomposition into a product of generalized observability and controllability matrices

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless- or dissipative system from a given noise-free trajectory; important special cases are passive- and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; state-space equations are then computed solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order mode

A bilinear differential forms approach to parametric structured state-space modelling

We use one-variable Loewner techniques to compute polynomial-parametric models for MIMO systems from vector-exponential data gathered at various points in the parameter space. Instrumental in our approach are the connections between vector-exponential modelling via bilinear differential forms and the Loewner framework