Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control
Abstract
This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficients in both subsystems. In controller design, we circumvent the need to directly solve coupled time-varying parabolic-hyperbolic kernel equations by employing an analytic pre-defined gain function and a time-varying Volterra kernel function to design the control law explicitly. In stability analysis, to address the simultaneous challenges of Dirichlet boundary disturbances and time-varying coefficients, we employ the square root of a time-varying positive definite matrix and a superlinear function to construct a nonquadratic Lyapunov function for the ODE and a generalized Lyapunov functional for the PDE, respectively, in the target system, thereby establishing the ISS in the L2-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.
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BibTeX
@misc{bi2026inputtostate,
title = {{Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control}},
author = {Yongchun Bi and Jun Zheng and Guchuan Zhu and Jiye Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06599},
eprint = {2609.06599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06599},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control
AU - Yongchun Bi
AU - Jun Zheng
AU - Guchuan Zhu
AU - Jiye Zhang
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06599
UR - https://arxiv.org/abs/2609.06599
AB - This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficients in both subsystems. In controller design, we circumvent the need to directly solve coupled time-varying parabolic-hyperbolic kernel equations by employing an analytic pre-defined gain function and a time-varying Volterra kernel function to design the control law explicitly. In stability analysis, to address the simultaneous challenges of Dirichlet boundary disturbances and time-varying coefficients, we employ the square root of a time-varying positive definite matrix and a superlinear function to construct a nonquadratic Lyapunov function for the ODE and a generalized Lyapunov functional for the PDE, respectively, in the target system, thereby establishing the ISS in the L^2-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.
ER -