Two-stage controller design with integral action and decoupling

Two-stage stabilizing controller design methods that achieve type-m integral action and diagonal input-output transfer-functions are developed for linear, time-invariant, multi-input multi-output feedback systems. Integral action can be achieved with the proposed configurations if and only if the given plant is full row-rank and has no transmission zeros at zero. All stabilizing controllers with at least m integrators in each output channel are explicitly characterized. A parametrization of all decoupling controllers which also achieve type-m integral action is obtained