On the Implementation of Two-Parameter Stabilizing Controllers Using Stable-Block Input-Output Feedback Structures

Abstract

This paper a universal implementation method for continuous- and discrete-time two-parameter (2-DOF) stabilizing controllers using exclusively stable constituent blocks. The framework is valid for all regular SISO and MIMO plants, particularly those failing to satisfy the parity interlacing property where unstable controllers are unavoidable. Unlike existing algebraic approaches that compromise parametric design freedom to force sub-block stability, the proposed method preserves design precedence. By leveraging the Youla-Ku\v{c}era parametrization within input-output (I/O) feedback topologies, we decouple synthesis from implementation. This allows physical performance specifications to drive the controller design, which is subsequently realized via a cyclic configuration of stable blocks. This architecture yields key engineering advantages, including localized anti-windup, simplified initialization, and improved numerical robustness.