Modal structure under a specific feedback law

A recently presented pole placement algorithm is extended to provide a complete closed-loop modal analysis of a linear dynamic system. The algorithm, which is iterative in nature, constructs the closed-loop feedback gain matrix in steps from submatrices generated by the algorithm. These submatrices can be used not just for the construction of the gain matrix but, also, to derive the left and right eigenvectors of the closed-loop system as well. This derivation is done as a by-product of the pole-placement effort and is also iterative in nature following the same general steps of the pole-placement algorithm itself. The availability of the left and right eigenvectors can be further exploited to derive transition matrices and transfer matrices as well.