Well-posedness and stability of non-autonomous semilinear input-output systems

Abstract

We establish well-posedness results for non-autonomous semilinear input-output systems, the central assumption being the scattering-passivity of the considered semilinear system. We consider both systems with distributed control and observation and systems with boundary control and observation. Applications are given to nonlinearly controlled collocated systems and to nonlinearly controlled port-Hamiltonian systems.

31 pages, 1 figure. Added an application example (Section 5.1). Also, added proofs (Section 3.1 and 4.1) and stability statements to the well-posedness theorems (Section 3.2 and 4.2). And finally, removed some errors, namely a slight imprecision in the definition of generalized solutions and outputs (see discussion at the very end of Section 2.1) and an error in the assumptions of Corollary 5.1