Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization
Year: 2026
Type: preprint
Abstract: The paper introduces a successive backstepping observer design for strictly feedforward parabolic PDE-ODE systems, in which the coupling structure determines the order of error stabilization and the corresponding transformations. First, a transformation based on a virtual measurement stabilizes the ODE observer error subsystem, which is most distal from the measurement, while decoupling it from the PDE error state. Second, a Volterra integral transformation is employed to stabilize the PDE error subsystem and to map the overall error dynamics into a cascade of exponentially stable ODE and PDE subsystems. The design is shown to be dual to a recently proposed multi-step state feedback design for parabolic PDE-ODE systems in strict feedback form, thus explaining the structure of the presented observer design.
Source: arXiv (Cornell University)
Author: Gehring, Nicole
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G7032374119, G801936796
OpenAlex ID: W7204940989