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arXiv · 2607.03838

Regional Input-to-State Stability for Systems on Riemannian Manifolds

Li Deng·Yuan Wang
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Abstract

In this paper, we study regional input-to-state stability (regional ISS) for time-varying control systems evolving on connected and complete Riemannian manifolds with a prescribed open state domain. Using the Riemannian distance, we formulate the notion of a region of ISS and introduce an ISS-Lyapunov function. We prove that the existence of such a function implies regional ISS in an explicitly estimated geodesic ball and yields a corresponding admissible input bound. Under additional geometric and dynamical assumptions, this region can be enlarged to the largest geodesic ball centered at the equilibrium point and contained in the prescribed state domain. Examples under the Euclidean and hyperbolic metrics show that different Riemannian metrics may lead to different estimates for the same system.

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Li Deng, Yuan Wang. 2026-09-12. Regional Input-to-State Stability for Systems on Riemannian Manifolds. https://arxiv.org/abs/2607.03838

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