\(H_ 2\) optimal controllers with measurement feedback for discrete-time systems: Flexibility in closed-loop pole placement (Q1356127)

For a general \(H_2\) optimal control problem, first all \(H_2\) optimal measurement-feedback controllers are characterized and parameterized, and the 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. In contrast to the continuous-time case, for discrete-time systems, one basically encounters two different problems: firstly the minimization of the closed-loop \(H_2\) norm over all strictly proper internally stabilizing controllers and secondly the minimization of the closed-loop \(H_2\) norm over all proper internally stabilizing controllers. This is so because, for discrete-time systems, the minima for these two problems are in general different. 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 exists many \(H_2\) optimal measurement-feedback controllers, utilizing such flexibility and freedom, allows to place the closed-loop poles at more desirable locations white still preserving \(H_2\) optimality. All the design algorithms developed here are easily computer-implementable.