scholarly journals Decay rate estimates for a weak viscoelastic beam equation with time-varying delay

2014 ◽  
Vol 31 ◽  
pp. 46-51 ◽  
Author(s):  
Sun Hye Park
Keyword(s):  
Decay Rate ◽  
Beam Equation ◽  
Time Varying ◽  
Viscoelastic Beam ◽  
Time Varying Delay ◽  
Varying Delay

scholarly journals On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. Cong ◽  
Z.-B. Sheng
Keyword(s):  
Exponential Stability ◽  
Decay Rate ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Perturbation Approach ◽  
Time Varying ◽  
Fast Subsystem ◽  
Time Varying Delay ◽  
Slack Matrices ◽  
Varying Delay

We are interested in the exponential stability of the descriptor system, which is composed of the slow and fast subsystems with time-varying delay. In computing a kind of Lyapunov functional, we employ a necessary number of slack matrices to render the balance and to yield the convexity condition for reducing the conservatism and dealing with the case of time-varying delay. Therefore, we can get the decay rate of the slow variables. Moreover, we characterize the effect of the fast subsystem on the derived decay rate and then prove the fast variables to decay exponentially through a perturbation approach. Finally, we provide an example to demonstrate the effectiveness of the method.

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