$H_2$ optimal controllers with measurement feedback for discrete-time systems : flexibility in closed-loop pole placement

For a general H2 optimal control problem, at first all H2 optimal measurement feedback controllers are characterized and parameterized, and then attention is focused on controllers with estimator based architecture. The H2 optimal control problem with strictly proper controllers and the H2 optimal control problem with proper controllers are essentially different and hence clearly delineated. Next, estimator based H2 optimal controllers are characterized and parameterized. Also, systematic methods of designing them are presented. Three different estimator structures, prediction, current, and reduced order estimators, are considered. Since in general there exist many H2 optimal measurement feedback controllers, utilizing such flexibility and freedom, one can place the closed loop poles at more desirable locations while still preserving H2 optimality. All the design algorithms developed here are easily computer implementable. Key words: H2 Optimal Control, Multivariable Control, Discrete Time Systems