Robust observability for regular linear systems under nonlinear perturbation

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.

Keywords

• Admissible observation operator
• exact observability
• nonlinear semigroup
• regular linear system