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Nonlinear J-lossless conjugation and factorization

Nonlinear J-lossless conjugation and factorization
Nonlinear J-lossless conjugation and factorization
A new definition of nonlinear local J-lossless factorization is introduced, which plays a crucial role in nonlinear H control theory. Sufficient (and in two special cases also necessary) conditions for the existence of this factorization and state-space formulae of the factor systems are given here. The main tools for the J-lossless factorization are the local right and left J-lossless conjugations, introduced in this paper. The former corresponds to the standard linear J-lossless conjugation, while the latter has no counterpart in the linear theory where it is completely dual to the former one and hence conceptually redundant. In the nonlinear case, however, this duality is much weaker and therefore the left J-lossless conjugation is essential for solving the local J-lossless factorization for unstable systems. This factorization requires a transformation of the given system to a special form and solving two independent Hamilton-Jacobi partial differential equations. Solutions of the two Hamilton-Jacobi equations have to satisfy a simple coupling condition.
1049-8923
869-893
Baramov, L.
e4425a9c-2e31-4761-855c-91895363b7c6
Kimura, H.
2c968a31-76c4-4d28-8145-871266b1d431
Baramov, L.
e4425a9c-2e31-4761-855c-91895363b7c6
Kimura, H.
2c968a31-76c4-4d28-8145-871266b1d431

Baramov, L. and Kimura, H. (1996) Nonlinear J-lossless conjugation and factorization. International Journal of Robust and Nonlinear Control, 6, 869-893.

Record type: Article

Abstract

A new definition of nonlinear local J-lossless factorization is introduced, which plays a crucial role in nonlinear H control theory. Sufficient (and in two special cases also necessary) conditions for the existence of this factorization and state-space formulae of the factor systems are given here. The main tools for the J-lossless factorization are the local right and left J-lossless conjugations, introduced in this paper. The former corresponds to the standard linear J-lossless conjugation, while the latter has no counterpart in the linear theory where it is completely dual to the former one and hence conceptually redundant. In the nonlinear case, however, this duality is much weaker and therefore the left J-lossless conjugation is essential for solving the local J-lossless factorization for unstable systems. This factorization requires a transformation of the given system to a special form and solving two independent Hamilton-Jacobi partial differential equations. Solutions of the two Hamilton-Jacobi equations have to satisfy a simple coupling condition.

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Published date: 1996
Organisations: Electronics & Computer Science

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Local EPrints ID: 252463
URI: http://eprints.soton.ac.uk/id/eprint/252463
ISSN: 1049-8923
PURE UUID: fe0c3737-ebe2-4570-af51-4038b2660851

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Date deposited: 29 Jan 2000
Last modified: 08 Jan 2022 11:44

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Contributors

Author: L. Baramov
Author: H. Kimura

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