On Block roots of matrix polynomials based MIMO control system design

In this paper we are going to introduce a new control design algorithms based on the theory of matrix polynomials. The first procedure is called Block decoupling control which is based on the spectral factors of the denominator of the right matrix fraction description (RMFD), the advantages of this control are the non-interacted behavior, simplicity in control design and low order controller is obtained due to the cancellation property of the proposed algorithm. The second control is called MIMO PID controller design via the placement of Block roots with the help of Diophantine equation resolution, the later systematic procedure retains both regulation and tracking objectives with small gains and minimum error.