No-weight design of H2 controllers for square plants

In this study, a reduced complexity design procedure for H₂ control problems of square plants is presented. First, all stabilising controllers are parameterised. Second, a modified inner-outer factorisation is defined for unstable plants and analytical formulas are developed. Third, the unique optimal controller is analytically derived by utilising the proposed parameterisation and the modified inner-outer factorisation. Finally, a simple tuning rule is developed for quantitative performance and robustness. The proposed procedure has three features: First, it is a no-weight design. The designer is not required to choose a weight. Second, this is an analytical design. The designer can directly use the developed design formulas and thus the design procedure is significantly simplified. Third, this is a quantitative design. The designer can design the controller for quantitative performance such as overshoot or stability margin. Numerical examples are given to illustrate the proposed method.