Electron. J. Diff. Equ., Vol. 2015 (2015), No. 218, pp. 1-14.

Robust observability for regular linear systems under nonlinear perturbation

Weisheng Jiang, Bin Liu, Zhibing Zhang

Abstract:
In this article, we consider the admissibility and exact observability of a class of semilinear systems obtained by nonlinear perturbation for regular linear systems. We obtain the well-posedness of the semilinear system and the admissibility of the observation operator for the nonlinear semigroup, the solution semigroup of the semilinear system. Further, we obtain the robustness of the exact observability with respect to nonlinear perturbations when the Lipschitz constant is small enough. Finally, we give two examples to illustrate the obtained results.

Submitted July 18, 2015. Published August 20, 2015.
Math Subject Classifications: 47H20, 93B07, 93C25, 93C73.
Key Words: Admissible observation operator; exact observability; nonlinear semigroup; regular linear system.

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Weisheng Jiang
College of Mathematics and Statistics
Chongqing University
Chongqing 401331, China
email: wsjiang@cqu.edu.cn
Bin Liu
College of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: liubin@ctbu.edu.cn
Zhibing Zhang
College of Mathematics and Statistics
Chongqing University
Chongqing 401331, China
email: zhibing0719@163.com

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