The function [bound,muinfo,RPmargin]=fRP(M,om) computes the robust performance margins for the uncertain plant M and for the frequency grid \omega=[\omega_1,\ldots,\omega_N]. It returns the \mu-ssv upper- and lower-bounds by means of the mussv command from the Robust Control Toolbox. The outputs are:

  • bound: A structure with the lower- and upper-bounds for each frequency \omega\in[\omega_1,\ldots,\omega_N].
  • muinfo: The \mu-information obtained during the computations.
  • RPmargin: The robust performance margins.

If specifying the 3rd inputs as fRP(M,om,U_\mathrm{sc})</em>, one can rescale the analysis as follows. Given the uncertain plant

    \[M=\left(\begin{array}{cc}M_{11}&M_{12}\\  M_{21}&M_{22}\end{array}\right)\]

the uncertainty scaling factor, <em>U_\mathrm{sc}</em>, scales the size of the uncertainty such that

\mu_\mathbf{\Delta}(M_{11}(i\omega))\leq\dfrac{\gamma}{U_\mathrm{sc}}, \mu_\mathbf{\Delta}(M(i\omega))\leq\gamma for all \Delta\in\mathbf{\Delta} with \|\Delta\|_\infty<\dfrac{U_\mathrm{sc}}{\gamma}.

If not specified, U_\mathrm{sc} is set to its default value U_\mathrm{sc}=1.

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