LTV parametric uncertainties (arbitrarily fast varying, full block)

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

  • name: ‘Delta’
  • Uncertainty block \Delta(\delta) is defined by the map


    with \delta=\left(\delta_1,\delta_2,\delta_3,\delta_4\right)^T
  • bounds: \delta_i\in[-0.1,0.1], i\in\{1,2,3,4\}
  • Input channels of M connecting the uncertainty block: 1,2
  • Outputs channels of M connecting the uncertainty block: 1,2

This uncertainty can be created as follows:

H{1}  = [1,0;0,1];
H{2}  = [1,1;0,0];
H{3}  = [0,1;1,0];
H{4}  = [1,0;1,0];

La    = polydec(pvec('box',0.1*[-1,1;-1,1;-1,1;-1,1]))';

Delta = iqcdelta('Delta','InputChannel',1:2,'OutputChannel',1:2,'TimeInvTimeVar','TV','Structure','FB', 'UncertaintyMap',H,'Polytope',La);

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

For this multiplier you have to choose the type of relaxation. At the moment you can choose between four options. In this example, we wish to consider the convex hull relaxation, which can be specified as (though a typical analysis would start with the less computationally demanding ‘DG’ option):

Delta = iqcassign(Delta,'ultv','RelaxationType','CH');

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