A popular alternative approach to loopsyn loop shaping is H∞ mixed-sensitivity loop shaping, which is implemented by the Robust Control Toolbox™ software command:
where (see MIXSYN H∞ Mixed-Sensitivity Loop Shaping Ty1 u1):
The term is called a mixed-sensitivity cost function because it penalizes both sensitivity S(s) and complementary sensitivity T(s). Loop shaping is achieved when you choose W1 to have the target loop shape for frequencies ω < ωc, and you choose 1/W3 to be the target for ω > ωc. In choosing design specifications W1 and W3 for a mixsyn controller design, you need to ensure that your 0 dB crossover frequency for the Bode plot of W1 is below the 0 dB crossover frequency of 1/W3, as shown in Singular Value Specifications on L, S, and T, so that there is a gap for the desired loop shape Gd to pass between the performance bound W1 and your robustness bound . Otherwise, your performance and robustness requirements will not be achievable.