Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control
Year: 2026
Type: preprint
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 $L^2$-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.
Source: arXiv (Cornell University)
Authors: Bi, Yongchun, Zheng, Jun, Zhu, Guchuan, Zhang, Jiye
Institutions: Southwest Jiaotong University, Polytechnique Montréal
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212015735