An aggregative optimal pole-placement procedure for discrete-time linear systems

A sequential optimal control procedure which simultaneously assigns one by one the real eigenvalues and pair by pair the complex eigenvalues of a multivariable discrete-time linear system is presented. The method is capable of assigning all or a subset of the closed-loop eigenvalues and simultaneously results in gain-matrices which satisfy a quadratic cost criterion with suitable weighting matrices. Analytical algorithms are proposed for both real and complex closed-loop eigenvalues which are tested on an illustrative example.