The class udel is defined by diagonally repeated delay uncertainties of the form:
- Type 1:
- Type 2:
- 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.
|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 .
|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  for the details on the mathematical derivation of the IQC-multiplier.