Computation of Sylvester and Stein matrix equations' solutions by Iterative Decreasing Dimension Method

Abstract

Sylvester matrix equation and the Stein matrix equation which have very important applications in the stability analysis of continuous-time and discrete-time linear systems, respectively are studied. The solutions of these equations be possible demonstrated by a number of methods. Been one of them transformation to the system of linear equation was examined. Algorithms that provide transformation to $Ax=f$ system of linear equation was introduced. Iterative Decreasing Dimension Method ($IDDM$) algorithm was applicated for the solution of the obtained system. The $IDDM$ algorithm has been evaluated according to the Gaussian elimination type algorithms. The $IDDM$ algorithm is evade from divisor of zero based on its algorithmic structure. Depending on the study, codes for calculation were prepared in the MAPLE program code development environment.