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A Behavioral Approach to Passivity and Bounded Realness Preserving Balanced Truncation with Error Bounds

A Behavioral Approach to Passivity and Bounded Realness Preserving Balanced Truncation with Error Bounds
A Behavioral Approach to Passivity and Bounded Realness Preserving Balanced Truncation with Error Bounds
In this paper we revisit the problems of passivity and bounded realness preserving model reduction by balanced truncation. In the behavioral framework, these problems can be considered as special cases of balanced truncation of strictly half line dissipative system behaviors, where the number of input variables of the behavior is equal to the positive signature of the supply rate. Instead of input-state-output representations, the balancing algorithm uses normalized driving variable representations of the behavior. We show that the diagonal elements of the minimal solution of the balanced algebraic Riccati equation are the singular values of the map that assigns to each past trajectory the optimal storage extracting future continuation. Since the future behavior is only an indefinite inner product space, the term singular values should be interpreted here in a generalized sense. We establish some new error bounds for this model reduction method.
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b

Trentelman, Harry L. and Rapisarda, Paolo (2009) A Behavioral Approach to Passivity and Bounded Realness Preserving Balanced Truncation with Error Bounds. 48th IEEE Conference on Decision and Control, Shanghai, China. 15 - 18 Dec 2009. (In Press)

Record type: Conference or Workshop Item (Paper)

Abstract

In this paper we revisit the problems of passivity and bounded realness preserving model reduction by balanced truncation. In the behavioral framework, these problems can be considered as special cases of balanced truncation of strictly half line dissipative system behaviors, where the number of input variables of the behavior is equal to the positive signature of the supply rate. Instead of input-state-output representations, the balancing algorithm uses normalized driving variable representations of the behavior. We show that the diagonal elements of the minimal solution of the balanced algebraic Riccati equation are the singular values of the map that assigns to each past trajectory the optimal storage extracting future continuation. Since the future behavior is only an indefinite inner product space, the term singular values should be interpreted here in a generalized sense. We establish some new error bounds for this model reduction method.

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Accepted/In Press date: December 2009
Venue - Dates: 48th IEEE Conference on Decision and Control, Shanghai, China, 2009-12-15 - 2009-12-18
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 267960
URI: https://eprints.soton.ac.uk/id/eprint/267960
PURE UUID: 904969bd-9868-4676-b5f1-8bc69d0575da

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Date deposited: 26 Sep 2009 08:30
Last modified: 18 Feb 2019 17:31

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