Semilinear observation systems

In this paper, we introduce locally Lipschitz observation systems for nonlinear semigroups and show that they can be represented by an ‘admissible’ nonlinear output operator defined on a suitable subspace. In the semilinear case, this concept fits well to the Lebesgue extension known from linear system theory. For semilinear systems, we show robustness of exact observability near equilibria under locally small Lipschitz perturbations. Finally, we apply our results to a damped nonlinear plate equation and a semilinear thermo-elastic system.