A Solution to the diagonalization problem by constant precompensator and dynamic output feedback

A solution is obtained for the problem of diagonalization (row by row decoupling) by a constant precompensator and a dynamic output feedback compensator of a p x m linear time-invariant system. The solvability condition is compact and concerns the dimension of a single subspace defined via the concepts of “essential rows” and “static kernels“ associated with the transfer matrix. A characterization of the set of all solutions to the problem is also given. In solving this dynamic feedback problem, we also obtain a complete solution to its state-feedback counterpart, namely, the restricted state-feedback problem of diagonalization. © 1989 IEEE