Nonlinear locally distributed feedback stabilization

Shui-Hung Hou; Qing-Xu Yan

doi:10.3934/jimo.2008.4.67

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2008, Volume 4, Issue 1: 67-79. Doi: 10.3934/jimo.2008.4.67

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Nonlinear locally distributed feedback stabilization

Shui-Hung Hou^1, and
Qing-Xu Yan^2,

1.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
2.
Information Engineering School, China Geosciences University, Beijing 100083

Received: July 31, 2006

Revised: October 31, 2007

Published: December 2007

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Abstract

The stabilization problem of a nonuniform Timoshenko beam with nonlinear locally distributed feedback controls is considered. By means of nonlinear semigroup theory, energy-perturbation approach and piecewise multiplier method it is shown that the energy of the closed loop system decays exponentially or in the rate of negative power of time.

Keywords:

Nonuniform Timoshenko beam,
Locally distributed feedback stabilization,
Nonlinear semigroups,
Piecewise exponential multiplier,
Energy perturbation method.

Mathematics Subject Classification: 93C20, 93D20.

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