Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Deng, Li, Wang, Yuan
Institution: Southwest Jiaotong University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167614475