Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

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

  • Li Deng
  • Yuan Wang
Open at sourcePDFDOICite

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.

Related

  1. Stability of optimal transport on sub-Riemannian manifolds
    Bang-Xian Han, Zhuo-Nan Zhu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  2. Riemannian Density-Driven Optimal Control: Tangent-Space LQR for Second-Order Multi-Agent Systems on Curved Manifolds
    Kooktae Lee, Ruchika Singh
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  3. Input-to-state stability of second-order port-Hamiltonian systems under nonlinear dynamic boundary feedback
    Bouchra Elghazi, Birgit Jacob, Christophe Prieur
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  4. Non-Fragile Guaranteed Cost Control for Uncertain Fractional Delay Systems of Variable Order with Time-Varying Control Input Delays: A Possibly Stability Analysis
    Alireza Alfi, Zahra Sadat Aghayan, António M. Lopes
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  5. Spline interpolation on compact riemannian manifolds
    Charlie Sire, Mike Pereira, Thomas Romary
    Numerical AlgorithmsPeer-reviewedLicence not statedStatisticsHAL

Cite

BibTeXRIS
BibTeX
@misc{deng2026regional,
  title = {{Regional Input-to-State Stability for Systems on Riemannian Manifolds}},
  author = {Li Deng and Yuan Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.03838},
  eprint = {2607.03838},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.03838},
}
RIS
TY  - UNPB
TI  - Regional Input-to-State Stability for Systems on Riemannian Manifolds
AU  - Li Deng
AU  - Yuan Wang
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.03838
UR  - https://arxiv.org/abs/2607.03838
AB  - 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.
ER  -