scholarly journals Quasi-stability property and attractors for a semilinear Timoshenko system

2016 ◽  
Vol 36 (11) ◽  
pp. 6117-6132 ◽  
Author(s):  
Luci H. Fatori ◽  
Marcio A. Jorge Silva ◽  
Vando Narciso
Keyword(s):  
Stability Property ◽  
Timoshenko System

Long-time dynamics of a class of nonlocal extensible beams with time delay

2021 ◽  
pp. 108128652110194
Author(s):  
Fengjuan Meng ◽  
Cuncai Liu ◽  
Chang Zhang
Keyword(s):  
Time Delay ◽  
Stability Property ◽  
Beam Equation ◽  
Exponential Attractors ◽  
Time Dynamics ◽  
Bounded Smooth Domain ◽  
Finite Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
Long Time Dynamics

This work is devoted to the following nonlocal extensible beam equation with time delay: [Formula: see text] on a bounded smooth domain [Formula: see text]. The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.

scholarly journals Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system

2010 ◽  
Vol 23 (3) ◽  
pp. 414-430 ◽  
Author(s):  
F. D. Araruna ◽  
P. Braz E Silva ◽  
E. Zuazua
Keyword(s):  
Timoshenko System

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

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