Discrete-time-ILQ optimal feedback design by polynomial matrices

This paper gives a design method for discrete-time optimal regulators. A state feedback is designed which allocates part of the closed-loop poles exactly at specified points inside the unit circle, and is linear quadratic (LQ) optimal for some weightings at the same time. This is achieved by placing the rest of the poles sufficiently close to the origin, thereby satisfying a modified circle criterion, a solution to the inverse problem of discrete-time LQ control. The obtained design method is a discrete-time version of a continous-time ILQ (inverse LQ) method by polynomial matrices.