The class ultv_rb is defined by LTV rate-bounded parametric uncertainties of the form:
- , .
- is assumed to be star convex: .
The ultv_rb class can be defined by
Just specifying defines a rate-bounded LTV parametric uncertainty with 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.
|NumberOfRepetitions|| Specify the number of repetitions of the uncertainty (default = 1). |
Note: In case of more than one uncertainty, one needs to specify the number of repetitions as .
|Bounds||Specify the domain on which the uncertainty is defined (default = ).|
|RateBounds||Specify the domain on which the uncertainty is rate-bounded (default = ).|
|Polytope||Alternatively, instead of using the option Bounds/RateBounds one can specify the option Polytope:|
Note: It is always assumed that the 0 is contained in the set.
|InputChannel/ OutputChannel||Specify which input and output channels of the uncertain plant are affected by . For each , 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 . Note here thatthe row length of and equals the number of repetitions of . The option InputChannel/ OutputChannel should then be specified as a cell:
|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).|
Note: In case of multiple diagonally repeated uncertainties, one can specify one common length, or a different one for each respectively as or . See link for further details.
|PoleLocation||Specify the pole location of the basis function (default = -1). |
Note: In case of multiple diagonally repeated uncertainties, one can specify one common pole-location, or a different one for each respectively as or . See link for further details.
|SampleTime||Specify the sample time (default = 0).|
|RelaxationType||Specify the relaxation type. Options are (default = ‘DG’):|
– DG-scalings: ‘DG’
– Convex hull relaxation: ‘CH’
– Partial convexity: ‘PC’
– Zeroth order Polya relaxation: ‘ZP’
|RelaxationProp||Specify the relaxation constraint type. Options are (default = ‘S’)|
– Static relaxation constraints: ‘S’
– Dynamic relaxation constraints: ‘D’
|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 5.4 of  for the details on the mathematical derivation of the IQC-multiplier.