A Recursive Algorithm for Reducing the Order of Controller while Guaranteeing Performance

In this paper, a procedure for the recursive reduction of the order of the stabilizing controller is introduced for SISO systems. Since all achievable closed loop maps are affine in the Q (Youla) parameter, we devise a sufficient condition for order reduction: Suppose there exists a Q parameter to induce a pole zero cancellation in the closed loop map to decrease the order of the closed loop system by m, then the corresponding controller is reduced in order by m. By appropriately choosing Q, we formulate a procedure for the recursive reduction of the order of the stabilizing controller and guarantee a performance describable through a complex stabilization technique.