The class *udel* is defined by diagonally repeated delay uncertainties of the form:

- Type 1:
- Type 2:

Here

- is the Laplace operator
- is the number of repetitions
- with being the maximum delay time.

The *udel* class can be defined by

Just specifying defines an LTI diagonally repeated delay uncertainty of Type 1, which has a maximum delay of second and which is repeated once.

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 |

DelayType | Specify the type of delay operator (i.e., Type 1 or Type 2) (Default = 1). |

DelayTime | Specify the maximum time delay for (default = 1). |

NumberOfRepetitions | Specify the number of repetitions of the uncertainty (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. |

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

AddIQC | Specify whether to add an additional LMI constraint for obtaining potentially improved results at the cost of more computational complexity.Note: The default value is ‘yes’. |

MstrictlyProp | Specify whether the part of the plant that is seem by the uncertainty satisfies . If so, one of the LMI constraints on the IQC (see previous property) can be dropped, allowing for more freedom in the optimization problem.Note 1: The default value is ‘no’. Note 2: This test is automatically turned to ‘yes’ in the IQC analysis if indeed . |

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