H2 optimal controllers with measurement feedback for continuous-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 observer based architecture. An important problem that can be coined as an H₂ optimal control problem with simultaneous pole placement, is formulated and solved. That is, since in general there exist many H₂ 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 H₂ optimality. We discuss here only full order observer based controllers. The discussion of reduced order observer based controllers follows along the same lines