Model reduction of nonlinear systems with bounded incremental $L_2$ gain

Bart  Besselink; Nathan van de Wouw; Henk Nijmeijer

doi:10.1109/CDC.2011.6160907

Model reduction of nonlinear systems with bounded incremental $L_2$ gain

Bart Besselink, Nathan van de Wouw, Henk Nijmeijer

Research output: Contribution to conference › Paper › Academic

4 Citations (Scopus)

Abstract

A model reduction procedure for a class of nonlinear systems is presented in the current paper. Nonlinear systems are considered that can be decomposed into a linear subsystem of high order and a nonlinear subsystem of relatively low order, allowing for an approach in which only the linear subsystem is reduced using well-developed linear model reduction techniques. For this approach, conditions for stability of the reduced-order nonlinear system are given, as well as an error bound in terms of the L 2 signal norm. Herein, the nonlinear subsystem is assumed to have a bounded incremental L 2 gain, which proves to be a crucial property in the derivation of the results. The method is illustrated by means of an example.

Original language	English
Pages	7170-7175
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2011.6160907
Publication status	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12-Dec-2011 → 15-Dec-2011

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/2011 → 15/12/2011

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10.1109/CDC.2011.6160907

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Model reduction of nonlinear systems with bounded incremental L2 gain
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title = "Model reduction of nonlinear systems with bounded incremental $L_2$ gain",

abstract = "A model reduction procedure for a class of nonlinear systems is presented in the current paper. Nonlinear systems are considered that can be decomposed into a linear subsystem of high order and a nonlinear subsystem of relatively low order, allowing for an approach in which only the linear subsystem is reduced using well-developed linear model reduction techniques. For this approach, conditions for stability of the reduced-order nonlinear system are given, as well as an error bound in terms of the L 2 signal norm. Herein, the nonlinear subsystem is assumed to have a bounded incremental L 2 gain, which proves to be a crucial property in the derivation of the results. The method is illustrated by means of an example.",

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doi = "10.1109/CDC.2011.6160907",

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AU - van de Wouw, Nathan

AU - Nijmeijer, Henk

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AB - A model reduction procedure for a class of nonlinear systems is presented in the current paper. Nonlinear systems are considered that can be decomposed into a linear subsystem of high order and a nonlinear subsystem of relatively low order, allowing for an approach in which only the linear subsystem is reduced using well-developed linear model reduction techniques. For this approach, conditions for stability of the reduced-order nonlinear system are given, as well as an error bound in terms of the L 2 signal norm. Herein, the nonlinear subsystem is assumed to have a bounded incremental L 2 gain, which proves to be a crucial property in the derivation of the results. The method is illustrated by means of an example.

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