A constructive algorithm for the complete set of compensators for two-dimensional feedback system design

In the recent factorization approach to linear feedback system design, it has been found that in order to completely solve a generalized Ω-stabilization problem, a coprime condition in the ring of Ω-stable transfer functions must be solved. In this note, two-dimensional (2- D) systems are considered, and this Ω-stable coprime condition is solved for Ω-stable rings. A well-known 2-D zero-coprime condition is a special case of this condition. This is the first constructive method for obtaining the complete set of solutions, or compensators, for 2-D feedback system design. Some examples of systems treated as 2-D systems are: temporal-spatial, spatial-spatial, delay-differential, multipass, etc.