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

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 direct ap- proach to state a controller form fails already for a very simple MIMO example. Next, a generalised hyperbolic controller form with different variants is proposed and a new flatnesss-based scheme to compute said form is presented. Therein, the system is treated in an algebraic setting where generalised polynomials with real exponents are used to describe the predictions and delays in the system. The proposed algorithm is then applied to the motivating example.