Partial pole placement by discrete-time LQ control and its sampled-data performance

This paper gives a design method for discrete-time optimal control, and then studies its performance from a sampled-data point of view. First, as discrete-time control, a state feedback gain is designed which places 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. Secondly, it is checked whether thus obtained (pure) discrete-time feedback is again optimal as a sampled-data control system; i.e., whether it minimizes some continuous-time performance index.