Discrete optimal control with aggregate pole placement

A recursive algorithm for designing an optimal modal controller is presented for the case of discrete MIMO systems. A basic method is developed, followed by an aggregative procedure which gives a computational simplicity. The state weighting matrix in the quadratic performance criterion and the feedback gain matrix are calculated without solving the algebraic matrix Riccati equation. At the same time the eigenspectrum of the closed-loop system is placed at some predefined location. The case of assigning real and distinct poles is developed entirely and is illustrated with a numerical example.