Norm-bounded uncertainties

In this section it is demonstrated how to create a norm-bounded nonlinearity block. To do so, suppose that this nonlinearity has the following properties:

Name: ‘Delta’
Size: $3\times 4$
Norm-bound: 0.2
Input channels of $M$ connecting the uncertainty block: $1:3$
Outputs channels of $M$ connecting the uncertainty block: $1:4$

This uncertainty can be created as follows:

delta = iqcdelta('delta','LinNonlin','NL','InputChannel', 1:3,'OutputChannel',1:4,'NormBound',0.2);

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

This can be specified as:

delta = iqcassign(delta,'usg');

Note: In general, for norm-bounded nonlinearities, you can only consider static multipliers. However, in case your integrand of the IQC-multiplier is non-negative for all frequencies $\omega\in\mathbb{R}\cup\{\infty\}$ , you can also allow for dynamics in the multiplier, and, hence, set the length of the basis function to values larger than 1 (see [1] for further details). This can be specified as:

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