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January  2008, 4(1): 67-79. doi: 10.3934/jimo.2008.4.67

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, China
2. 

Information Engineering School, China Geosciences University, Beijing 100083, China

Received  August 2006 Revised  November 2007 Published  January 2008

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: Locally distributed feedback stabilization, Nonlinear semigroups, Piecewise exponential multiplier, Energy perturbation method., Nonuniform Timoshenko beam.
Mathematics Subject Classification: 93C20, 93D2.
Citation: Shui-Hung Hou, Qing-Xu Yan. Nonlinear locally distributed feedback stabilization. Journal of Industrial & Management Optimization, 2008, 4 (1) : 67-79. doi: 10.3934/jimo.2008.4.67
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