A simultaneous assignment methodology of right/left eigenstructures

In the sense of eigenstructure (eigenvalues/eigenvectors) assignment, the effectiveness and disturbance suppressibility of a controller are mainly dependent on the left eigenstructure (eigenvalues/left eigenvectors) of a system. However, the disturbance decouplability is governed by the right eigenstructure (eigenvalues/right eigenvectors) of the system. In order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a simultaneous assignment methodology of the right and left eigenstructures is proposed. The biorthogonality property between the left and right modal matrices of a system as well as the relations between the achievable right modal matrix and states selection matrices are used to develop the methodology. The proposed simultaneous eigenstructures assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. An L-1011 flight control application is presented to illustrate the usefulness of the proposed methodology.