Lur'e feedback systems with both unbounded control and observation: Well-posedness and stability using nonlinear semigroups

This paper is a complement of information to Grabowski and Callier (2006) [1]. A SISO Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static incremental sector type controller is considered. Well-posedness and a criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a novel nonlinear semigroup approach. A quadratic form Lyapunov functional is considered via a Lur'e type linear operator inequality. A sufficient strict circle criterion of solvability of the latter is found, using the solution of an operator Riccati equation by a novel self contained exposition, via reciprocal systems with bounded generating operators as recently studied and used by R.F. Curtain. The noncoercive case is finally considered using, in a novel way, LaSalle's invariance principle.