H2 optimal controllers with measurement feedback for discrete-time systems: Flexibility in closed-loop pole placement

Abstract

For a general H 2 optimal control problem, first all H 2 optimal measurement-feedback controllers are characterized and parameterized, 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 different and hence clearly delineated. Next, estimator-based H 2 optimal controllers are characterized and parameterized. Systematic methods of designing them are also presented. Three different estimator structures, namely prediction, current and reduced-order estimators, are considered. Since in general there exist many H 2 optimal measurement-feedback controllers, utilizing such flexibility 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-implementable.