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arXiv · 2511.13546

On the controller form for linear hyperbolic MIMO systems with dynamic boundary conditions

Stefan Ecklebe·Frank Woittennek
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Abstract

This contribution develops an algebraic approach to obtain a controller form for a class of linear hyperbolic MIMO systems, bidirectionally coupled with a linear ODE system at the unactuated boundary. After a short summary of established controller forms for SISO and MIMO ODE as well as SISO hyperbolic PDE systems, it is shown that the approach to state a controller form for SISO systems cannot easily be transferred to the MIMO case as it already fails for a very simple example. Next, a generalised hyperbolic controller form with different variants is proposed and a new flatness-based scheme to compute said form is presented. Therein, the system is treated in an algebraic setting where quasipolynomials are used to express the predictions and delays in the system. The proposed algorithm is then applied to the motivating example.

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Stefan Ecklebe, Frank Woittennek. 2025-11-17. On the controller form for linear hyperbolic MIMO systems with dynamic boundary conditions. https://arxiv.org/abs/2511.13546

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