DERIVATION OF THE GLOVER-DOYLE ALGORITHMS FOR GENERAL H-INFINITY CONTROL-PROBLEMS

We show that the Glover-Doyle algorithm can be formulated simply by us ing the (J,J')-lossless factorization method and chain scattering matr ix description. This algorithm was first stated by Glover and Doyle in 1988. Because the corresponding diagonal block of the (J,J')lossless matrix in the general 4-block H-infinity control problem of the Glover -Doyle algorithm is not square, a new type of chain scattering matrix description is developed. With this description in hand, we obtain two types of state-space solution, which are similar to each other. Thus a similarity transformation between these solutions in the 4-block H-i nfinity control problem can also be obtained. The main idea of the sol ution is illustrated by means of block diagrams.