Compensator design via the separation principle for a class of semilinear evolution equations

UDC 517.9 We establish a compensator design via the separation principle in the practical sense for a class of semilinear evolution equations in Hilbert spaces. Under a restriction imposed on the perturbation, which is bounded by an integrable function, we propose a nonlinear time-varying practical Luenberger observer to estimate the states of the system and prove that the Luenberger observer based on the linear controller stabilizes the system. An illustrative example is given to demonstrate the applicability of our theoretical results.