RECURSIVE ALGORITHMS FOR SOLVING A CLASS OF NONLINEAR MATRIX EQUATIONS WITH APPLICATIONS TO CERTAIN SENSITIVITY OPTIMIZATION PROBLEMS

This paper is concerned with solving a class of nonlinear algebraic ma trix equations. Two recursive algorithms are proposed in terms of matr ix difference equations and are studied. A set of initial values is ch aracterized, from which the convergence of the algorithms can be guara nteed. Based on the general results, several effective algorithms are presented to compute L(2)-sensitivity optimal realizations, as well as Euclidean norm balancing realizations, of a given linear system. A lo cally exponential convergence property is proved for one of them. As i s shown by simulation in this paper, these algorithms prove to be far more practical for digital computer implementation than the gradient f lows previously proposed.