Numerically reliable computing for the row by row decoupling problem with stability

Abstract

This is the first of two papers on the row by row decoupling problem and the triangular decoupling problem. In this paper we study the row by row decoupling problem with stability in control theory. We first prove a nice reduction property for the row by row decoupling problem with stability and then develop a numerically reliable method for solving it. The basis of our main results is some condensed forms under orthogonal transformations, which can be implemented in numerically stable ways. Hence our results lead to numerically reliable methods for solving the studied problem using existing numerical linear algebra software such as MATLAB. In the sequel [SIAM J. Matrix Anal. Appl., 23 (2002), pp. 1171-1182], we will consider a related problem - the triangular decoupling problem - and parameterize all solutions for it.