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

For a general H₂ optimal control problem, first all H ₂ optimal measurement feedback controllers are characterized and parameterized. 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. 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