Geodesic
Stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance
Electronic journal of differential equations, Tome 2015 (2015)
We consider the stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance. The time varying extended state observer (ESO) is designed to estimate the disturbance. Based on the estimated disturbance, we obtain an explicit controller by applying the backstepping method. It is shown that the closed-loop system of the 1-D hyperbolic differential equation is asymptotically stable under this controller. This result is illustrated by simulation examples.
Classification : 49K20, 93C20
Keywords: extended state observer, disturbance rejection, backstepping method, 1-D hyperbolic equation 
@article{EJDE_2015__2015__a9,
     author = {Zhang,  Xiaoying and Chai,  Shugen},
     title = {Stabilization for {1-D} hyperbolic differential equations with boundary input including a nonlinear disturbance},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1350.93077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a9/}
}
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TI  - Stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance
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%A Chai,  Shugen
%T Stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance
%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a9/
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Zhang,  Xiaoying; Chai,  Shugen. Stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a9/