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arXiv · 2607.08637

Aclass of incrementally scattering-passive nonlinear systems

Shantanu Singh·George Weiss·Marius Tucsnak
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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.

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Shantanu Singh, George Weiss, Marius Tucsnak. 2026-07-09. Aclass of incrementally scattering-passive nonlinear systems. https://doi.org/10.1016/j.automatica.2022.110369

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