The file *Demo_013.m* is found in IQClabâ€™s folder *demos*. This demo performs regional analysis following the numerical example reported in [22].

Here the uncertain system is given by with and the open-loop LTI plant

where

.

The demo file *Demo_013.m* computes the “smallest” ellipsoid that contains the output trajectory against disturbances with . The results are obtained with the following lines of code

% Define uncertain plant M = ... % Define uncertainty block de = iqcdelta('u','InputChannel',1, 'OutputChannel',1,'Bounds',[-1,1]); de = iqcassign(de,'ultis','Length',4); % Define performance block pe = iqcdelta('pe','InputChannel',2,'OutputChannel', 2:3,'ChannelClass','P','PerfMetric','e2z'); % Perform IQC-analysis prob = iqcinvariance(M,{de,pe},'SolChk','on', 'eps',1e-6);

The demo then generates the following figure depicting the ellipsoids obtained for different lengths of the basis function (red lines), the tight ellipsoid (black line) and various worst-case trajectories with and (i.e., the worst case uncertainty).

As can be seen, the IQC-analysis produces non-conservative (tight) ellipsoids for higher lengths of the basis function (dynamic multipliers), while for basis length 1 (static multipliers) we obtain more conservative results, which clearly demonstrates the benefit of considering dynamics in the multipliers.