Electron. J. Diff. Equ., Vol. 2015 (2015), No. 66, pp. 1-10.

Stabilization for 1-D hyperbolic differential equations with boundary input including a nonlinear disturbance

Xiaoying Zhang, Shugen Chai

Abstract:
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.

Submitted December 12, 2014. Published March 18, 2015.
Math Subject Classifications: 49K20, 93C20.
Key Words: Extended state observer; disturbance rejection; backstepping method; 1-D hyperbolic equation.

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Xiaoying Zhang
School of Mathematical Science
Shanxi University
email: zxybetter@163.com
Shugen Chai
School of Mathematical Science
Shanxi University
Taiyuan 030006, China
email: sgchai@sxu.edu.cn, Phone +863517010555

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