This paper contains an algorithm for the numerical computation of the local feedback stabilizing matrix via linear programming for a system (A. B-d) consisting of two interconnected subsystems. Following the initial definition of the global system and its two subsystems in the state space, an equivalent system defined in the operator domain by an appropriate polynomial matrix description (PMD) is determined. This is based on the intercontrollability matrix D(s) of system (A, B-d) and the determination of its kernel U(s), Applying a suitable transformation to the PMD system matrix M-d(s), and based on linear programming methods, an algorithm with which the coefficients of the feedback stabilizing matrix could be computed is finally proposed.