Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor

2007 ◽  
Vol 56 (2) ◽  
pp. 122-132 ◽  
Author(s):  
Ilyasse Aksikas ◽  
Joseph J. Winkin ◽  
Denis Dochain
Keyword(s):  
Asymptotic Stability ◽  
Semilinear Systems ◽  
Infinite Dimensional

Compensation of Time-Varying Input and State Delays for Nonlinear Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Time Varying ◽  
Feedback Systems ◽  
Feedback Controllers ◽  
Stabilizing Controller ◽  
Numerical Examples ◽  
Infinite Dimensional ◽  
State Delays ◽  
Main Challenge

We consider general nonlinear systems with time-varying input and state delays for which we design predictor-based feedback controllers. Based on a time-varying infinite-dimensional backstepping transformation that we introduce, our controller achieves global asymptotic stability in the presence of a time-varying input delay, which is proved with the aid of a strict Lyapunov function that we construct. Then, we “backstep” one time-varying integrator and we design a globally stabilizing controller for nonlinear strict-feedback systems with time-varying delays on the virtual inputs. The main challenge in this case is the construction of the backstepping transformations since the predictors for different states use different prediction windows. Our designs are illustrated by three numerical examples, including unicycle stabilization.

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