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

The numerical computation of the simultaneous disturbance decoupling and ro w-by-row decoupling problem is considered. Based on a condensed form for th e system matrices the solvability of the simultaneous disturbance decouplin g and row-by-row decoupling problem is reduced to the verification of an in teger equality and the nonsingularity of a lower-dimensional constant matri x. The condensed form we use is computed using only orthogonal transformati ons, which can be implemented in a numerically stable way. Hence, it leads directly to an effective numerical method for solving the disturbance decou pling and row-by-row decoupling problem using existing tools such as LAPACK and Matlab. Our result complements existing geometric and structural appro aches which are of a theoretical nature and are not suitable for numerical computation. (C) 2000 Elsevier Science Inc. All rights reserved. AMS classi fication: 93B05; 93B40; 93B52; 65F35.