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Determination of time dependent factors of coefficients in fractional diffusion equations
Exponential stabilization of Timoshenko beam with input and output delays
1. | School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China |
2. | Department of Mathematics, Tianjin University, Tianjin 300072 |
References:
[1] |
T. Faria, On a planar system modelling a neuron network with memory, J. Differential Equations, 168 (2000), 129-149.
doi: 10.1006/jdeq.2000.3881. |
[2] |
T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, J. Differential Equations, 244 (2008), 1049-1079.
doi: 10.1016/j.jde.2007.12.005. |
[3] |
Guo, Y. Chen and J. Wu, Two-parameter bifurcations in a network of two neurons with multiple delays, J. Differential Equations, 244 (2008), 444-486.
doi: 10.1016/j.jde.2007.09.008. |
[4] |
B. Z. Guo, C. Z. Xu and H. Hammouri, Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation, ESAIM:Control, Optimization and Calculus of Variations, 18 (2012), 22-35.
doi: 10.1051/cocv/2010044. |
[5] |
Z. J. Han and G. Q. Xu, Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks, ESAIM:Control, Optimization and Calculus of Variations, 17 (2010), 552-574.
doi: 10.1051/cocv/2010009. |
[6] |
J. U. Kim and Y. Renardy, Boundary control of the Timoshenko beam, SIAM. J. Control Optim., 25 (1987), 1417-1429.
doi: 10.1137/0325078. |
[7] |
X. F. Liu and G. Q. Xu, Exponenntial stabilization for Timoshenko beam with distributed delay in the boundary control, Abstract and Applied Analysis, (2013), Art. ID 726794, 15 pp.
doi: 10.1155/2013/726794. |
[8] |
S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feednacks, SIAM Journal on Control and Optimization, 45 (2006), 1561-1585.
doi: 10.1137/060648891. |
[9] |
S. Nicaise and J. Valein, Stabilitization of the wave equation on 1-d networks with a delay term in the nodal feedbacks, Networks and Heterogeneous Media, 2 (2007), 425-479.
doi: 10.3934/nhm.2007.2.425. |
[10] |
S. Nicaise and C. Pignotti, Stabilitization of the wave equation with boundary or internal distributed delay, Differential and Integral Equation, 21 (2008), 935-958. |
[11] |
G. Stepan, Retarded dynamical system: stability and characteristic functions, Longman Scientific and Technical, John Wiley and Sons, Inc., New York, (1989), 136-147. |
[12] |
Y. F. Shang and G. Q. Xu, Stabilization of an Euler-Bernoulli beam with input delay in the boundary control, Systems and Control letters, 61 (2012), 1069-1078.
doi: 10.1016/j.sysconle.2012.07.012. |
[13] |
Y. F. Shang, G. Q. Xu and Y. L. Chen, Stability analysis of Euler-Bernoulli beam with input delay in the boundary control, Asian Journal of Control, 14 (2012), 186-196.
doi: 10.1002/asjc.279. |
[14] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Basel Hoston Berlin: Birkhaüser, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[15] |
G. Q. Xu, S. P. Yung and L. K. Li, Stabilization of wave systems with input delay in the boundary control, ESAIM: Control,Optimisation and Calculus of Variations, 12 (2006), 70-785.
doi: 10.1051/cocv:2006021. |
[16] |
G. Q. Xu and H. X. Wang, Stabilization of Timoshenko beam system with delay in the boundary control, INT. J. Control, 86 (2013), 1165-1178.
doi: 10.1080/00207179.2013.787494. |
[17] |
R. Yafia, Danamics and numerical simulations in a production and development of red blood cells model with one delay, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 582-592.
doi: 10.1016/j.cnsns.2007.08.012. |
show all references
References:
[1] |
T. Faria, On a planar system modelling a neuron network with memory, J. Differential Equations, 168 (2000), 129-149.
doi: 10.1006/jdeq.2000.3881. |
[2] |
T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, J. Differential Equations, 244 (2008), 1049-1079.
doi: 10.1016/j.jde.2007.12.005. |
[3] |
Guo, Y. Chen and J. Wu, Two-parameter bifurcations in a network of two neurons with multiple delays, J. Differential Equations, 244 (2008), 444-486.
doi: 10.1016/j.jde.2007.09.008. |
[4] |
B. Z. Guo, C. Z. Xu and H. Hammouri, Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation, ESAIM:Control, Optimization and Calculus of Variations, 18 (2012), 22-35.
doi: 10.1051/cocv/2010044. |
[5] |
Z. J. Han and G. Q. Xu, Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks, ESAIM:Control, Optimization and Calculus of Variations, 17 (2010), 552-574.
doi: 10.1051/cocv/2010009. |
[6] |
J. U. Kim and Y. Renardy, Boundary control of the Timoshenko beam, SIAM. J. Control Optim., 25 (1987), 1417-1429.
doi: 10.1137/0325078. |
[7] |
X. F. Liu and G. Q. Xu, Exponenntial stabilization for Timoshenko beam with distributed delay in the boundary control, Abstract and Applied Analysis, (2013), Art. ID 726794, 15 pp.
doi: 10.1155/2013/726794. |
[8] |
S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feednacks, SIAM Journal on Control and Optimization, 45 (2006), 1561-1585.
doi: 10.1137/060648891. |
[9] |
S. Nicaise and J. Valein, Stabilitization of the wave equation on 1-d networks with a delay term in the nodal feedbacks, Networks and Heterogeneous Media, 2 (2007), 425-479.
doi: 10.3934/nhm.2007.2.425. |
[10] |
S. Nicaise and C. Pignotti, Stabilitization of the wave equation with boundary or internal distributed delay, Differential and Integral Equation, 21 (2008), 935-958. |
[11] |
G. Stepan, Retarded dynamical system: stability and characteristic functions, Longman Scientific and Technical, John Wiley and Sons, Inc., New York, (1989), 136-147. |
[12] |
Y. F. Shang and G. Q. Xu, Stabilization of an Euler-Bernoulli beam with input delay in the boundary control, Systems and Control letters, 61 (2012), 1069-1078.
doi: 10.1016/j.sysconle.2012.07.012. |
[13] |
Y. F. Shang, G. Q. Xu and Y. L. Chen, Stability analysis of Euler-Bernoulli beam with input delay in the boundary control, Asian Journal of Control, 14 (2012), 186-196.
doi: 10.1002/asjc.279. |
[14] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Basel Hoston Berlin: Birkhaüser, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[15] |
G. Q. Xu, S. P. Yung and L. K. Li, Stabilization of wave systems with input delay in the boundary control, ESAIM: Control,Optimisation and Calculus of Variations, 12 (2006), 70-785.
doi: 10.1051/cocv:2006021. |
[16] |
G. Q. Xu and H. X. Wang, Stabilization of Timoshenko beam system with delay in the boundary control, INT. J. Control, 86 (2013), 1165-1178.
doi: 10.1080/00207179.2013.787494. |
[17] |
R. Yafia, Danamics and numerical simulations in a production and development of red blood cells model with one delay, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 582-592.
doi: 10.1016/j.cnsns.2007.08.012. |
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