4.1. THE HIMATEXAMPLE 139
complex valued blocks.
The upper and lower bounds of the µfunction are returned in bnds. Also returned are
the scaling matrices, Dand Dinv, corresponding to the upper bound. The smallest
destabilizing perturbation at each frequency is returned as Delta. The variable sens is
the sensitivity of the upper bound to the Dand Dinv scaling matrices. This will be
useful as a weighting function for fitting transfer functions to the Dand Dinv scaling
blk = [2,2;2,2]
[bnds1,D1,D1inv,Delta1,sens1] = mu(g1g,blk)
comment blk "perturbation block structure"
comment bnds1 "mu bounds: iteration 1"
comment D1 "D scale: iteration 1"
comment D1inv "D inverse scale: iteration 1"
comment Delta1 "worst case perturbation: iteration 1"
comment sens1 "D scale sensitivity: iteration 1"
We plot the maximumsingular value and µon the same plot. The performance and
stability specifications have been achieved if µis less than one at all frequencies.
gph4 = ctrlplot(g1gs(1,1),{log,line style=4});
gph4 = ctrlplot(bnds1,gph4,{log,line style=[1,3]});
gph4 = plot(gph4,{title="Max. singular value and mu comparison",...
legend=["max. singular value";"mu upper bound";...
"mu lower bound"],!grid})?