2D feedback system design: the tracking and disturbance rejection problems

This paper considers the generalized regulator and tracking problems for linear 2D systems where the measured outputs are not necessarily the same as the controlled outputs and either 1DOF (degree-of-freedom) or 2DOF controller may be used. Necessary and sufficient solvability conditions are given for various cases of this general configuration, which reveal that, just as in the 1D case, the concept of skew Ω-primeness for 2D polynomial and rational function matrices introduced previously by the authors plays a central role in 2D regulator and tracking problems. Furthermore, several other well-used configurations are also investigated as special cases