Uniqueness of the general mixed H2/H∞ optimal controller

A convex analysis approach to the general mixed H₂/H _∞ optimal control design with single and multiple H_∞ constraints is developed. The system consists of a plant and stable weights on the H₂ and H_∞ transfer functions, and is linear-time-invariant. The controller order is relaxed to an unknown but optimal order and the nature of the solution is examined. It is shown that the optimal controller is unique through the use of a Youla parametrization and convex analysis. Uniqueness is combined with the Kuhn-Tucker conditions to characterise the solution to the mixed problem with a finite set of H_∞ constraints. Finally, the nature of a fixed order controller is examined