Journal Article

Stability theory for infinite-dimensional linear systems based on an extension method

JINGBO WU

in IMA Journal of Mathematical Control and Information

Volume 15, issue 2, pages 117-132
Published in print June 1998 | ISSN: 0265-0754
Published online June 1998 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/15.2.117
Stability theory for infinite-dimensional linear systems based on an extension method

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The state for a homogeneous infinite-dimensional linear system can be extended to the dual of a countably Hilbertian space with graph topology. The stability theory for the extension of the system is illustrated. We prove that the exponential growth bound of the extended system is the infimum of ω such that the resolvent is a funtion of finite order in the half plane Re λ ≥ ω. Relationships between various notions of stability of the original system and of its extension are considered. For the question of exponential stability for physical problem, the original theory may lead to opposite results while the extension method will avoid the contradiction.

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Subjects: Mathematics

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