The class *usg* is defined by uncertainties/nonlinearities of the form with

- Dimension
- Norm bound

The *us*g class can be defined by

Just specifying defines a scalar uncertainty/ nonlinearity with norm-bound .

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

Property | Description |

Dimension | Specify the dimension of the uncertainty/ nonlinearity (default = 1). |

NormBounds | Specify the norm-bound , of the uncertainty/ nonlinearity (default = 1). |

InputChannel/ OutputChannel | Specify which input and output channels of the uncertain plant are affected by . The channels should be specified as:
Here the order of the channels is not relevant, while , respectively denote the and in- and output channel of the uncertain plant . |

Property | Description |

BasisFunctionType | Specify the type of basis function to be used in the multiplier (default = 1). See link for further details. |

Length | Specify the length of the basis function (default = 1). See link for further details. Note: It is not always allowed to set . |

PoleLocation | Specify the pole location of the basis function (default = -1). See link for further details. |

SampleTime | Specify the sample time (default = 0). |

PrimalDual | Specify 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. |

*Note: See Section 5.7 of [1] for the details on the mathematical derivation of the IQC-multiplier.*