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A popular alternative approach to loopsyn loop shaping is H_{∞} mixed-sensitivity loop shaping, which is implemented by the Robust Control Toolbox™ software command:
K=mixsyn(G,W1,[],W3)
With mixsyn controller synthesis, your performance and stability robustness specifications equations (2-2) and (2-4) are combined into a single infinity norm specification of the form
$${\Vert {T}_{{y}_{1}{u}_{1}}\Vert}_{\infty}\le 1$$
$${T}_{{y}_{1}{u}_{1}}\stackrel{def}{=}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\begin{array}{cc}{W}_{1}& S\\ {W}_{3}& T\end{array}\right].$$
The term $${\Vert {T}_{{y}_{1}{u}_{1}}\Vert}_{\infty}$$ 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 W_{1} to have the target loop shape for frequencies ω < ω_{c}, and you choose 1/W_{3} to be the target for ω > ω_{c}. In choosing design specifications W_{1} and W_{3} for a mixsyn controller design, you need to ensure that your 0 dB crossover frequency for the Bode plot of W_{1} is below the 0 dB crossover frequency of 1/W_{3}, 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 W_{1 }and your robustness bound $${W}_{3}^{-1}$$. Otherwise, your performance and robustness requirements will not be achievable.