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Stabilization and a class of functionals for linear parabolic control systems

Published online by Cambridge University Press:  04 February 2010

Takao Nambu
Takao Nambu
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Kobe University, Nada, Kobe 657-8501, Japan, (nambu@kobe-u.ac.jp)
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Abstract

In feedback stabilization studies, a control scheme is designed so that the ‘state’ of the system decays with a designated rate as t → ∞. Thus, any linear functional of the state also decays with at least the same decay rate. We study a class of linear parabolic systems, and show the existence of a feedback control scheme with a specific property such that some non-trivial linear functionals decay faster than the state. In constructing the control scheme, we also solve the new problem of an arbitrary allocation of the eigenvalues of some coefficient matrix which is subject to constraint, and give the necessary and sufficient condition in terms of controllability and observabililty assumptions. This is an essential extension of the celebrated 1967 theory of pole allocation by W. M. Wonham.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 153 - 174
Copyright
Copyright © Royal Society of Edinburgh 2010

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