LTI dynamic uncertainties

In this section it is demonstrated how to create a dynamic full-block LTI uncertainty block. To do so, suppose that this uncertainty has the following properties:

name: ‘delta’
size: $2\times 3$
norm-bound: 1
number of repetitions: 2
Input channels of $M$ connecting the uncertainty block: $1,2$ for the first block and $3,4$ for the second block
Outputs channels of $M$ connecting the uncertainty block: $1:3$ for the first block and $4:6$ for the second block

This uncertainty can be created as follows:

delta = iqcdelta('delta','StaticDynamic','D', 'Structure','FB','InputChannel',[1,2;3,4],'OutputChannel',[1:3;4:6],'NormBounds',1);

Alternatively, though in a more cumbersome way, you can also specify each block independently and then combine them with blkdiag as follows:

delta1 = iqcdelta('delta1','StaticDynamic','D','Structure', 'FB','InputChannel',[1,2],'OutputChannel',[1:3],'NormBounds',1);

delta2 = iqcdelta('delta1','StaticDynamic','D','Structure', 'FB','InputChannel',[3,4],'OutputChannel',[4:6],'NormBounds',1);

delta  = blkdiag('delta',delta1,delta2);

In a next step, you have to assign an IQC-multiplier. The appropriate class for this is called ultid (for details see here).

Now suppose you want the basis function have the following properties:

Length: 3 (this corresponds to a McMillan degree of 2)
Pole location: -1

This can be specified as:

delta = iqcassign(delta,'ultid','Length',2, 'PoleLocation',-1);