On lambda-matrices and their applications in MIMO control systems design

In the present paper, we have introduced 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 behaviour, simplicity in control design and low order controller is obtained due to the cancellation property of the proposed algorithm. The second control algorithm is the whole set of latent-structure assignment via the approaches of block root placement. Of course, the procedure has been developed even if the system is not block transformable, a process done with the aid of conversion between state space and matrix fraction description. The last method defined as a MIMO PID controller design via the placement of block roots with the help of Diophantine equation resolution, the latter systematic procedure retains both regulation and tracking objectives with small gains and minimum error.