The file Demo_006.m is found in IQClab’s folder demos. This demo performs an IQC robustness analysis for an uncertain plant that is affected by sector-bounded and slope-restricted scalar nonlinearities. Here it is possible to the following input:
The uncertainty block:
- 3 different sector-bounded scalar nonlinearities
- 3x repeated sector-bounded scalar nonlinearity
- 3 different sector-bounded and slope-restricted scalar nonlinearities
- 3x repeated sector-bounded and slope-restricted scalar nonlinearity
The uncertain system is given by with the open-loop LTI plant , where
, , , .
On the other hand, the uncertainty block is defined by:
- with ,
- with ,
If running scenarios 1. and 2., we obtain the results shown in the following two figures. As can be seen, considering three independent blocks leads to lower bounds on the worst-case -gains if compared to one block that is repeated trice. In addition, the third and fourth figure demonstrate the advantage of considering both a sector and a slope constraint (instead of just a sector constraint) in the analysis by the favour of the Zames-Falb multiplier.