An algorithm for Eigenvalue assignment in multi-input systems

Abstract

This paper describes a computational method for solving the problem of eigenvalue assignment in a multi-input linear system. The given system is first reduced to an upper block Hessenberg form by means of orthogonal state coordinate transformations. It is then shown how a sequence of state feedback matrices and orthogonal state coordinate transformations can be applied to obtain a block triangular structure for the resulting state matrix, where the matrices on the diagonal are square matrices in upper Hessenberg form and of dimensions equal to the controllability indices of the multi-input system. Furthermore, the structure of the corresponding input matrix is such that the problem of eigenvalue assignment in the multi-input system can be reduced to several single-input eigenvalue assignment problems where the dimensions of the single-input systems are equal to the controllability indices of the multi-input system.