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