Robust Observability For Regular Linear Systems Under Nonlinear Perturbation

In recent years, the problem of robust observability for observation systems hasbeen the concern of many scholars. However, the problem has been studied under linearperturbation. We will study this problem under nonlinear perturbation. This hasimportant theoretical significance and application value. Specifically, this paper mainlydiscusses the following two problems：（1）Under the condition of the nonlinear term satisfies global Lipschitz continuity,we solve the admissibility and exact observability of observation operator forsemigroups. A concrete example is given to describe the main results；（2）Under the condition of the nonlinear term satisfies local Lipschitz continuity,we obtain the well-posedness of semilinear closed-loop system.Because the regular linear systems are abstract forms of partial differential systemboundary observation and boundary control, therefore, our results can be applied to theboundary control of partial differential system nonlinearities. This also makes thesystem than the system research to the wider, more practical. In order to get theobservation operator with respect to the perturbation tolerance and exact observabilityof semigroups, use control operator with respect to the admissibility of semigroups ofoperators of the original system, and the input and output function of regular linearsystems with bounded.