A state observer is designed for a class of generalized Persidskii systems with nonlinear measurements, state disturbances, and output noise. We assume that all nonlinearities are diagonal and belong to a sector. The robust stability and convergence conditions for the estimation error are obtained by applying the theory of input-to-output stability. These conditions are established in the form of linear matrix inequalities. We provide numerical examples to demonstrate the efficacy and performances of the proposed observer.