NaN is not accepted since the estimation requires a valid initial value to start.
The following code works for me.
%grayboxmodeling
load sdata2 tt2
tt = tt2;
% State Space
A = [0 1 0 0
0 0 1 0
0 0 0 1
0 0 1 0];
B = [0
1
0
1];
C = eye(1,4);
D = zeros(1,1);
K = zeros(4,1);
x0 = [0;
0;
-0.03;
0];
Ts = 0.1;
init_sys = idss(A,B,C,D,K,x0,Ts);
apar = init_sys.Structure.A;
apar.Free(1,:) = false;
apar.Free(2,1) = false;
apar.Free(2,2) = false;
apar.Free(2,3) = true;
apar.Free(2,4) = false;
apar.Free(3,:) = false;
apar.Free(4,1) = false;
apar.Free(4,2) = false;
apar.Free(4,4) = false;
init_sys.Structure.A = apar;
bpar = init_sys.Structure.B;
bpar.Free(1,1) = false;
bpar.Free(3,1) = false;
init_sys.Structure.B = bpar;
init_sys.Structure.C.Free = false;
sysgray = ssest(tt,init_sys)
>> sysgray.A
ans =
0 1.0000 0 0
0 0 2.2653 0
0 0 0 1.0000
0 0 0.2710 0
