The function \psi=fBasis(l,p,n_r,type) creates minimum state space realizations for various basis functions that are used for the parametrization of IQC-multipliers. Here

  • l is the length of the basis function, which equals the McMillan degree m plus 1 (i.e., l=m+1).
  • p is the pole location of the basis function.
  • n_r is the number of diagonal repetitions of the basis function
  • type is the type of basis function. The current version includes 4 versions as specified next:

    \[\psi=\left(\begin{array}{c}1\\\frac{(i\omega+pl)}{(i\omega-pl)}\\ \frac{(i\omega+pl)^2}{ (i\omega-pl)^2}\\\vdots\\ \frac{(i\omega+pl)^l}{ (i\omega-pl)^l} \end{array}\right)\otimes I_{n_r}\]


    \[\psi=\left(\begin{array}{c}1\\ \frac{(i\omega)}{(i\omega-pl)^{l-1}}\\ \vdots\\\frac{(i\omega)^{l-1}}{(i\omega-pl)^{l-1}}\end{array}\right)\otimes I_{n_r}\]


    \[\psi=\left(\begin{array}{c}1\\\frac{1}{(i\omega-pl)}\\ \frac{1}{ (i\omega-pl)^2}\\\vdots\\ \frac{1}{(i\omega-pl)^l}\end{array}\right)\otimes I_{n_r}\]

type=4This is the complex conjugate of type=3 (i.e. \psi=-(type=3)^*).
type=5This is the discrete time version of type=1
type=6This is the discrete time version of type=2 (not yet implemented)
type=7 This is the discrete time version of type=3

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