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

Abstract

For a general H 2 optimal control problem, at first all H 2 optimal measurement feedback controllers are characterized and parameterized, and then attention is focused on controllers with observer-based architecture. Both full-order as well as reduced-order observer-based H 2 optimal controllers are characterized and parameterized. Also, systematic methods of designing them are presented. An important problem, coined as an H 2 optimal control problem with simultaneous pole placement, is formulated and solved. That is, since in general there exist many H 2 optimal measurement feedback controllers, utilizing such flexibility and freedom, we can solve the problem of simultaneously placing the closed-loop poles at desirable locations whenever possible while still preserving H 2 optimality. All the design algorithms developed here are easily computer implementable.