American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains
  • JIMO Home
  • This Issue
  • Next Article
    A mixed simulated annealing-genetic algorithm approach to the multi-buyer multi-item joint replenishment problem: advantages of meta-heuristics
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
[1]

Xiu-Fang Liu, Gen-Qi Xu. Exponential stabilization of Timoshenko beam with input and output delays. Mathematical Control & Related Fields, 2016, 6 (2) : 271-292. doi: 10.3934/mcrf.2016004
[2]

Kaïs Ammari, Mohamed Jellouli, Michel Mehrenberger. Feedback stabilization of a coupled string-beam system. Networks & Heterogeneous Media, 2009, 4 (1) : 19-34. doi: 10.3934/nhm.2009.4.19
[3]

Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1103-1119. doi: 10.3934/dcdss.2018063
[4]

M. Grasselli, Vittorino Pata, Giovanni Prouse. Longtime behavior of a viscoelastic Timoshenko beam. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 337-348. doi: 10.3934/dcds.2004.10.337
[5]

Ionuţ Munteanu. Exponential stabilization of the stochastic Burgers equation by boundary proportional feedback. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2173-2185. doi: 10.3934/dcds.2019091
[6]

Luis Barreira, Claudia Valls. Nonuniform exponential dichotomies and admissibility. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 39-53. doi: 10.3934/dcds.2011.30.39
[7]

Horst R. Thieme. Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 735-764. doi: 10.3934/dcds.1998.4.735
[8]

A. F. Almeida, M. M. Cavalcanti, J. P. Zanchetta. Exponential decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2039-2061. doi: 10.3934/cpaa.2018097
[9]

Adriana Flores de Almeida, Marcelo Moreira Cavalcanti, Janaina Pedroso Zanchetta. Exponential stability for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping. Evolution Equations & Control Theory, 2019, 8 (4) : 847-865. doi: 10.3934/eect.2019041
[10]

Arnaud Münch, Ademir Fernando Pazoto. Boundary stabilization of a nonlinear shallow beam: theory and numerical approximation. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 197-219. doi: 10.3934/dcdsb.2008.10.197
[11]

Huawen Ye, Honglei Xu. Global stabilization for ball-and-beam systems via state and partial state feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 17-29. doi: 10.3934/jimo.2016.12.17
[12]

Jeongho Ahn, David E. Stewart. A viscoelastic Timoshenko beam with dynamic frictionless impact. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 1-22. doi: 10.3934/dcdsb.2009.12.1
[13]

Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219
[14]

A. Rodríguez-Bernal. Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 1003-1032. doi: 10.3934/dcds.2009.25.1003
[15]

Nguyen H. Sau, Vu N. Phat. LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback. Journal of Industrial & Management Optimization, 2018, 14 (2) : 583-596. doi: 10.3934/jimo.2017061
[16]

Thomas I. Seidman, Houshi Li. A note on stabilization with saturating feedback. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 319-328. doi: 10.3934/dcds.2001.7.319
[17]

Carlos E. Kenig. The method of energy channels for nonlinear wave equations. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 1-15. doi: 10.3934/dcds.2019240
[18]

Luis Barreira, Claudia Valls. Admissibility versus nonuniform exponential behavior for noninvertible cocycles. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1297-1311. doi: 10.3934/dcds.2013.33.1297
[19]

Luis Barreira, Claudia Valls. Characterization of stable manifolds for nonuniform exponential dichotomies. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1025-1046. doi: 10.3934/dcds.2008.21.1025
[20]

Jin Zhang, Peter E. Kloeden, Meihua Yang, Chengkui Zhong. Global exponential κ-dissipative semigroups and exponential attraction. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3487-3502. doi: 10.3934/dcds.2017148

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences