ups: Passive uncertainties

The class ups is defined by uncertainties/nonlinearities of the form \Delta_\mathrm{ups}:L_2^{n_{in}}\rightarrow  L_2^{n_{out}} with

  • Dimension n_{out}\times n_{in}
  • \langle q,\Delta(q)\rangle\geq0

The ups class can be defined by

  • \Delta_\mathrm{ups}=ups('name')
  • \Delta_\mathrm{ups}=ups('name',varargin)

Just specifying \Delta_\mathrm{ups}=ups('name') defines a scalar passive uncertainty/ nonlinearity.

Specifying and/or changing properties proceeds as summarized in the following two tables for properties related to the uncertainty and to IQC-multiplier respectively.

Dimension Specify the dimension of the uncertainty/ nonlinearity (default = 1).
InputChannel/ OutputChannelSpecify which input and output channels of the uncertain plant are affected by \Delta_\mathrm{ups}. The channels should be specified as:

    \[\begin{array}{c} InputChannel=\left[\! \!  \! \begin{array}{ccc}C_{x}^{in}&\cdots&C_{y}^{in}\end{array} \!  \!  \! \right]\\OutputChannel=\left[ \!  \!  \! \begin{array}{ccc}C_{v}^{in}&\cdots&C_{w}^{in}\end{array} \!  \!  \! \right] \end{array}\]

Here the order of the channels is not relevant, while C_{m}^{in}, C_{n}^{out} respectively denote the m^{th} and n^{th} in- and output channel of the uncertain plant M.
Uncertainty characteristics

BasisFunctionTypeSpecify the type of basis function to be used in the multiplier (default = 1). See link for further details.
LengthSpecify the length of the basis function (default = 1). See link for further details.

Note: It is not always allowed to set Length>1.
PoleLocationSpecify the pole location of the basis function (default = -1). See link for further details.
SampleTimeSpecify the sample time (default = 0).
PrimalDualSpecify whether the multiplier should be a primal/dual parametrization (default = ‘Primal’).
– Primal multipliers: ‘Primal’
– Dual multipliers: ‘Dual’

Note: For a standard IQC-analysis, all multipliers must be primal ones.
Multiplier characteristics

Note: See Section 5.6 of [1] for the details on the mathematical derivation of the IQC-multiplier.

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