A Simplified Multi-Input Multi-Output Formulation for the Quantitative Feedback Theory

A simplified multi input/output formulation is developed for the quantitative feedback theory (QFT) for the 2 × 2 (n = 2) case. This formulation is consistent with traditional QFT philosophy where performance is specified for each individual closed-loop transfer function and control bandwidths are minimized. The simplified formulation turns the solution of a simultaneous robust stability and robust model matching problem into a two (n in general) step procedure of solving quadratic inequalities (whose coefficients are linear functions of the plants and the performance constraints); the traditional procedure requires six (n + n² in general) steps for a similar problem. A numerical example illustrates the simplified formulation and demonstrates its ability to offer useful insight in a control design.