Hi Philippe,
As best I can tell, the functional process is as follows. Referring to diagram under the "Description" of setDelayModel ...
1. Compute the frequency response of H in the usual way with H represented as an ordinary ss model. Here, the conversion to Hessenberg form would be used as normal. Call this result H(jw)
2. Compute the frequency response of the diagonal block of delays. Call this result D(jw).
3. Close the feedback loop of H(jw) and D(jw) in the usual way for all points in the frequency vector.
Unfortunately, steps 2 and 3 are hidden in mex file with no help or documenation, so the details of the implementation are unknown.
Example:
sys = feedback(tf(1,[1 1]),tf(1,1,'InputDelay',0.1)); % system with internal delay
[sysresp,w] = freqresp(sys); % its frequency response
% "by hand" computations
sysd = getDelayModel(sys);
H = frd(freqresp(ss(sysd.A,sysd.B,sysd.C,sysd.D),w),w);
D = frd(exp(-1j*0.1*w),w);
SYSresp = feedback(H,D,2,2,1);
SYSresp = SYSresp(1,1);
subplot(211)
semilogx(w,db(abs(squeeze(sysresp))),w,db(abs(squeeze(SYSresp.ResponseData))),'o')
subplot(212);
semilogx(w,180/pi*(angle(squeeze(sysresp))),w,180/pi*(angle(squeeze(SYSresp.ResponseData))),'o')
