The class *ultid* is defined by LTI diagonally repeated dynamic scaler or full-block uncertainties of the form:

Here

- is a stable LTI MIMO transfer matrix of dimension
- is the number of repetitions

The *ultid* class can be defined by

Just specifying defines an LTI dynamic uncertainty of dimension , which is repeated once and which satisfies .

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 |

Dimensions | Specify the size of the uncertainty as . Default = . |

NormBounds | Specify the -norm of the uncertainty by means of the constant (default = 1). |

NumberOf Repetitions | Specify the number of repetitions of the uncertainty (default = 1). |

InputChannel/ OutputChannel | Specify which input/output-channels of the uncertain plant are affected by the uncertainty. For each repetition of the block one should specify a row in the following matrix:
Here the order of the channels is not relevant, while and 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. |

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 5.1 of [1] for the details on the mathematical derivation of the IQC-multiplier.*