A class of incrementally scattering-passive nonlinear systems. (August 2022)

• Record Type: Journal Article
• Authors: Singh, Shantanu; Weiss, George; Tucsnak, Marius
• Is Part Of: Automatica. Volume 142(2022)
• Publication Date: 2022-08
• Subjects: Well-posed linear system -- Operator semigroup -- Lax–Phillips semigroup -- Scattering passive system -- Maximal monotone operator -- Crandall–Pazy theorem; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110369
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We investigate a special class of nonlinear infinite dimensional systems. These are obtained by subtracting a nonlinear maximal monotone (possibly multi-valued) operator ℳ from the semigroup generator of a scattering passive linear system. While the linear system may have unbounded linear damping (for instance, boundary damping) which is only densely defined, the nonlinear damping operator ℳ is assumed to be defined on the whole state space. We show that this new class of nonlinear infinite dimensional systems is well-posed and incrementally scattering passive. Our approach uses the theory of maximal monotone operators and the Crandall–Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax–Phillips type nonlinear semigroup that represents the whole system.