Stability of holomorphic semigroup systems under nonlinear boundary perturbations

Abstract: In this paper we re-study, by a different approach, the absolute stability of a class of holomorphic semigroup systems with nonlinear boundary feedback. A frequency criterion for equi-asymptotic stability in the large of the equilibrium of the closed loop has been recently derived in [3], by means of the Lyapunov function method. That stability result requires that the `infinite-sector' nonlinearities satisfy a suitable growth condition. In this paper we show that the previous restriction is unnecessary and that furthermore the result still holds true under a weaker frequency domain condition.