parametrization for a state space model

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karthik pakala 2017-5-15

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https://ww2.mathworks.cn/matlabcentral/answers/340405-parametrization-for-a-state-space-model

编辑： karthik pakala 2017-5-15

I have been using a software SIDPAC for aircraft system identification. In the estimation process I need to apply some constraints on the parameters that are being estimated. The state space model that is being used for the output error modelling is as follows,
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%code start
function [Y,X,A,B,C,D] = YawHeavDyn(p,U,w,x0,c)
n=c(1);
A=[p(1),p(2),n;...
   p(3),p(4),p(5);...
   n,p(6),p(7)];
ns=size(A,1);
B=[p(8),0;...
   p(9),p(10);...
   0,0];
C=[1,0,0;...
   0,1,0;...
   0,0,1];
D=[0,0;...
   0,0;...
   0,0];
[no,ni]=size(D);
nw=length(w);
jay=sqrt(-1);
jw=jay*w;
Y=zeros(nw,no);
X=zeros(nw,ns);
for i=1:nw,
  X(i,:)=((jw(i)*eye(ns,ns)-A)\(B*U(i,:).')).';
  Y(i,:)=(C*X(i,:).' + D*U(i,:).').';
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%code end
The parametric constraints that i have to apply are as follows,
p(7)=2*p(1)
p(10)=-p(5)
p(4)=p(3)
p(6)==[-inf 0]>>p(6) is less than zero.
[y7,p11,crb,rr]=fdoe('YawHeavDyn',p10,U,t,w,c,z);%%fdoe method used to estimate the output error model
p10-parameter vector
u-input vector
t-time vector
w-frequency vector
c-constant vector
z-output vector
Thanks in advance