Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 5 min ago
PreprintarXiv licencearXiv

Backstepping Stabilization of a Hyperbolic System with a Zero Characteristic Speed

  • Zhiqiang Wang
  • Wenhao Yang
Open at sourcePDFDOICite

Abstract

This paper investigates the boundary stabilization of a linear hyperbolic system with a zero characteristic speed. We address a case that cannot be stabilized by proportional boundary feedback and develop a backstepping design for the critical setting where the zero-speed subsystem has no intrinsic dissipation. To this end, we construct a Volterra transformation leading to a nonstandard integro-differential target system. Its asymptotic stability in L2 is established by both the Lyapunov-LaSalle method and a spectral semigroup argument. The backstepping kernel equations are explicitly solved, yielding an explicit boundary feedback law that asymptotically stabilizes the original system. Numerical simulations are provided to illustrate the effectiveness of the proposed control design.

Related

  1. Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization
    Nicole Gehring
    arXivPreprintCC BY-NC-SA 4.0Full textOptimisation & controlarXiv
  2. The Heavy Chain PDE: Rapid Stabilization by Backstepping
    Miroslav Krstic
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  3. Boundary stabilization of a moving interface in a 2 × 2 weakly hyperbolic system of balance laws: application to continuous sedimentation
    Mohand Ouidir Amirat, Vincent Andrieu, Mathieu Bajodek +1
    HALPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsOptimisation & controlHAL
  4. Boundary stabilization of a moving interface in a 2 x 2 weakly hyperbolic system of balance laws: application to continuous sedimentation
    Mohand Ouidir Amirat, Vincent Andrieu, Mathieu Bajodek +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  5. Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
    Johannes Droschl
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026backstepping,
  title = {{Backstepping Stabilization of a Hyperbolic System with a Zero Characteristic Speed}},
  author = {Zhiqiang Wang and Wenhao Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10835},
  eprint = {2610.10835},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10835},
}
RIS
TY  - UNPB
TI  - Backstepping Stabilization of a Hyperbolic System with a Zero Characteristic Speed
AU  - Zhiqiang Wang
AU  - Wenhao Yang
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10835
UR  - https://arxiv.org/abs/2610.10835
AB  - This paper investigates the boundary stabilization of a linear hyperbolic system with a zero characteristic speed. We address a case that cannot be stabilized by proportional boundary feedback and develop a backstepping design for the critical setting where the zero-speed subsystem has no intrinsic dissipation. To this end, we construct a Volterra transformation leading to a nonstandard integro-differential target system. Its asymptotic stability in L2 is established by both the Lyapunov-LaSalle method and a spectral semigroup argument. The backstepping kernel equations are explicitly solved, yielding an explicit boundary feedback law that asymptotically stabilizes the original system. Numerical simulations are provided to illustrate the effectiveness of the proposed control design.
ER  -