An algebraic approach to the control of spatially distributed systems: (2+1)D case with a deformable mirror example

In this paper we develop new results on control design for spatially distributed linear systems using an n- D systems approach. As a possible application example, we consider a deformable mirror used as a wavefront corrector in adaptive optical system. The first new results consist of stability analysis plus stability tests. This is followed by control law design in a polynomial setting where a Youla-Kucera parametrization of all stabilizing controllers is specialized to the objective of reducing vibrations of the mirror based on minimization of the H₂ system norm.