The class ultv is defined by LTV parametric uncertainties of the form:
- , are fixed matrices (having the same size as ).
- is a piecewise continuous time-varying parameter vector that takes its values form the (compact) polytope
- is assumed to be star convex:
The ultis class can be defined by
Just specifying defines an LTV parametric uncertainty on the interval , which is repeated once (i.e., and ).
Specifying and/or changing properties proceeds as summarized in the following two tables for properties related to the uncertainty and to IQC-multiplier respectively.
|Polytope||With the option Polytope on can specify the generator points of as|
Note: It is always assumed that the 0 is contained in the set.
|UncertaintyMap||Specify the matrices as a cell array . This defines the uncertainty map .|
Note: In case you wish to apply the DG-relaxation scheme, must be defined such that with , begin normalized.
|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:
|RelaxationType||Specify the relaxation type. Options are (default = ‘DG’):|
– DG-scalings: ‘DG’
– Convex hull relaxation: ‘CH’
– Partial convexity: ‘PC’
– Zeroth order Polya relaxation: ‘ZP’
|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 5.2 of  for the details on the mathematical derivation of the IQC-multiplier.