Determination of static diagonal controllers to achieve diagonal dominance for TITO systems at fixed frequencies

Most of the multivariable control systems include interactions between different input-output pairs. The control problem becomes more complex in case of significant interactions because single loop control solutions cannot be applied directly. In such cases, reducing the interactions with a pre-compensator can be accepted as the first step of design process. In this study, two input two output systems are discussed and sufficient conditions are derived to achieve diagonal dominance in case of static diagonal controllers. Moreover, a new algorithm is proposed to determine the controller gain regions that guarantees column and row diagonal dominance. Weighting factors are applied for both row and column diagonal conditions to obtain better results. Lastly, controller gain regions are plotted for a given TITO system to verify the effectiveness of the derived theoretical results.