Disturbance suppression and decoupling via eigenstructure assignment

An effective and disturbance suppressible controller can be obtained by assigning 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 this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, the concurrent assignment scheme of the left and right eigenstructure is proposed. The biorthogonality property between the left and right modal matrices of a system well as the relations between the achievable right modal matrix and states selection matrices are used to develop the scheme. The proposed concurrent eigenstructure assignment scheme 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. A numerical example is presented to illustrate the usefulness of the proposed scheme.