An LMI approach for reduced-order ℋ2 LTI controller synthesis

This paper presents a procedure to design reduced-order ℋ
₂
dynamic output feedback controllers for discrete-time linear time-invariant systems. Starting from a stabilizing full-order controller, novel sufficient linear matrix inequality conditions for the existence of reduced-order ℋ
₂
controllers are derived. The proposed approach can either be applied directly to compute a controller of desired order from the full-order result, or iteratively by reducing the controller order successively. Numerical experiments confirm the potential of the proposed controller design approach.