H 2 Optimal Controllers with Measurement Feedback forDiscrete - time Systems { Flexibility in Closed - loop Pole

For a general H 2 optimal control problem, at rst all H 2 optimal measurement feedback controllers are characterized and parame-terized, and then attention is focused on controllers with estimator based architecture. The H 2 optimal control problem with strictly proper controllers and the H 2 optimal control problem with proper controllers are essentially diierent and hence clearly delineated. Next, estimator based H 2 optimal controllers are characterized and parameterized. Also, systematic methods of designing them are presented. Three diierent estimator structures, prediction, current, and reduced order estimators, are considered. Since in general there exist many H 2 optimal measurement feedback controllers, utilizing such exibility and freedom, one can place the closed-loop poles at more desirable locations while still preserving H 2 optimality. All the design algorithms developed here are easily computer imple-mentable.