Hi Mohammad,
I confess that I can't explain how dss is implementing this uncertain, descriptor system. I'm particularly curious as to why sys has four states. Nevertheless, it does appear that sysp does, in fact, capture the simultaneous variation in k and JL
JM = 0.6; % Motor inertia
JL = 0.5; % Load inertia
k = 1200; % Torsional constant
kp = ureal('kp',k,'Percentage',[-10, 10]); % uncertain Torsional constant
JLp = ureal('JLp',JL,'Percentage',[-10, 10]);% uncertain Load inertia
% nominal system
A = [0 -k 0; 1 0 -1; 0 k 0];
E = diag([JM, 1, JL]); % Descriptor matrix
B = [1; 0; 0];
%Bd = [0; 0; -1];
C = [1 0 0];
D = 0;
sys0 = dss(A, B, C, D, E); % Use dss for descriptor systems
% perturbed system
Ap = [0 -kp 0; 1 0 -1; 0 kp 0];
Ep = diag([JM, 1, JLp]);
Bp = [1; 0; 0];
%Bdp = [0; 0; -1];
Cp = [1 0 0];
Dp = 0;
sys = dss(Ap, Bp, Cp, Dp, Ep)
omega = logspace(1,2,5000);
m=3;
[sysp,samples]=gridureal(sys,m);
samples.JLp
samples.kp
Here, I'll explicitly form the nominal and perturbed systems
pertvec = [0.9 1 1.1];
for ii = 1:3
pert = pertvec(ii);
temp{1,ii} = dss([0 -k*pert 0; 1 0 -1; 0 k*pert 0],B,C,D,diag([JM, 1, JL*pert]));
end
The Bode plots are identical
figure
bode(sysp,temp{:},omega)
figure
bode(sysp,temp{:},omega(omega>40))
