Formulations of the H∞ control problem by using chain scattering-matrix descriptions

By introducing coprime factors of the standard plant of an H^∞ control problem, we show the closed-loop transfer matrix resulting from a stabilising controller is equivalent to a (dual) pair of coupled chain scattering-matriees, one right chain scattering-matrix with one left chain scattering-matrix, with a free stable matrix. All H^∞ suboptimal controllers cam hence be generated by the solutions of only two coprime factorisations.