Assign IQC-multipliers

In a next step, you can proceed with preparing the IQC-analysis by assigning IQC-multipliers to the $\Delta$ -blocks. This can be done using the command iqcassign.

Indeed, IQC-multipliers can be easily assigned to objects created by iqcdelta by specifying

$\Delta=iqcassign(\Delta,'MultiplierType').$

The following multiplier classes are supported.

MultiplierType	Description	Link
ultid	Uncertain LTI dynamics	Details
ultis	LTI static diagonally repeated parametric uncertainties	Details
ultv	LTV parametric uncertainties	Details
ultv_rb	LTV rate bounded parametric uncertainties	Details
udel	Uncertain delay	Details
usbsr	Sector-bounded and slope restricted nonlinearities	Details
usg	Norm-bounded uncertainties (small-gain)	Details
ups	Passive uncertainties	Details

In addition, it is possible (an typically necessary) to assign additional multiplier properties to the uncertainties. For

$\Delta=iqcassign(\Delta,'MultiplierType',varargin),$

the input arguments come in pairs. Depending on the particular multiplier, the properties can that can be specified summarized in the following table.

Multiplier properties	Description
BasisFunctionType	Specify the type of basis function to be used in the multiplier (default = 1). Note: See link for further details.
Length	Specify the length of the basis function (default = 1). In case of multiple diagonally repeated uncertainties, one can specify one common length, or a different one for each $\delta_j$ respectively as $l$ or $[l_1,l_2,\ldots]$ . Note: See link for further details.
PoleLocation	Specify the pole location of the basis function (default = -1). In case of multiple diagonally repeated uncertainties, one can specify one common pole-location, or a different one for each $\delta_j$ respectively as $pl$ or $[pl_1,pl_2,\ldots]$ . Note: See link for further details.
SampleTime	Specify the sampling time (default = 0). In case of discrete time systems, one can specify the sampling time with a positive scalar or as $-1$ (unspecified).
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.

Previous page, Next page