Optimal Pole-Placement in Discrete Systems

This paper develops a technique to increase the damping in a closed-loop discrete time system by modifying a nominal linear quadratic performance criterion. The technique relies on the existence of more than one solution to the Discrete-time Algebraic Riccati Equation and on the modification of the nominal solution which leaves selected eigenvectors invariant. This increased damping is achieved by moving the nominal closed-loop eigenvalues to an exact location along the line segment connecting the nominal eigenvalues with the origin.