Abstract
It is well known that the ILQ (Inverse Linear Quadratic) method is a powerful tool for continuous-time control system design. The paper generalizes the existing polynomial ILQ method to the design of discrete-time regulator, and then studies its performance from a sampled-data point of view. First, given a discretized system, a state feedback gain is designed which places part of the closed-loop poles exactly at specified points inside the unit circle, and is 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 system; i.e., whether it minimizes some continuous-time performance index.
