On Mixed Galerkin Modeling for Controller Design of Boundary Control Systems

A mixed Galerkin formulation for reduced-order modeling is presented for controller design of distributed parameter systems with boundary inputs. A null space approach is established to yield appropriate trial and test functions by using candidate trial functions which are free from boundary conditions. The approach is applicable, with considerably mild conditions on the candidate trial functions, on the interior domain as well as its boundaries. It is shown that this modeling technique yields a finite dimensional descriptor system of index 1, that is equivalent to a state-space representation suitable for controller design model. Effectiveness of the proposed method is demonstrated by an example of a heat conduction rod using polynomial functions which are not preprocessed to meet the boundary conditions.