Improved Independent and Uniform Multivariable Gain and Phase Margins in $\mathcal {H}_{\infty }$/LTR Control

In this article, we presented guaranteed independent and uniform multivariable stability margins for the
$\mathcal {H}_{\infty }$
/LTR control, both in continuous and discrete time. In previous works, it was shown that the
$\mathcal {H}_{\infty }$
/LTR control generalizes the linear quadratic Gaussian (LQG)/LTR setup, allowing the designer to better impose bounds on the complementary sensitivity frequency peak in the loop-shaping procedure. In this article, we extend this result by showing that
$\mathcal {H}_{\infty }$
/LTR control is able to recover better robustness properties than those recovered in the LQG/LTR case. Numerical examples are presented for multivariable and monovariable cases.