A numerical solution for the simultaneous disturbance decoupling and row-by-row decoupling problem Original Research Article

The numerical computation of the simultaneous disturbance decoupling and row-by-row decoupling problem is considered. Based on a condensed form for the system matrices the solvability of the simultaneous disturbance decoupling and row-by-row decoupling problem is reduced to the verification of an integer equality and the nonsingularity of a lower-dimensional constant matrix. The condensed form we use is computed using only orthogonal transformations, which can be implemented in a numerically stable way. Hence, it leads directly to an effective numerical method for solving the disturbance decoupling and row-by-row decoupling problem using existing tools such as LAPACK and Matlab. Our result complements existing geometric and structural approaches which are of a theoretical nature and are not suitable for numerical computation.