Uniform stabilization of a thin elastic plate by nonlinear boundary feedback

2006 ◽  
pp. 305-317
Author(s):  
J. E. Lagnese
Keyword(s):  
Elastic Plate ◽  
Nonlinear Boundary ◽  
Thin Elastic Plate ◽  
Uniform Stabilization ◽  
Boundary Feedback ◽  
Nonlinear Boundary Feedback

Stabilization of an Axially Moving String by Nonlinear Boundary Feedback

1999 ◽  
Vol 121 (1) ◽  
pp. 117-121 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jinn-Wen Wu ◽  
Sheng-Luong Wu
Keyword(s):  
Nonlinear Boundary ◽  
Mechanical Energy ◽  
Control Laws ◽  
Axially Moving String ◽  
Boundary Feedback ◽  
Boundary Velocity ◽  
Total Mechanical Energy ◽  
Axially Moving ◽  
The Right ◽  
Nonlinear Boundary Feedback

In this paper, we consider the system modeled by an axially moving string and a mass-damper-spring (MDS) controller, applied at the right-hand side (RHS) boundary of the string. We are concerned with the nonlinear string and the effect of the control mechanism. We stabilize the system through a proposed boundary velocity feedback control law. Linear and nonlinear control laws through this controller are proposed. In this paper, we find that a linear boundary feedback caused the total mechanical energy of the system to decay an asymptotically, but it fails for an exponential decay. However, a nonlinear boundary feedback controller can stabilize the system exponentially. The asymptotic and exponential stability are verified.

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