Finding out optimum Q,R matrices and an Epsilon number of a given system.

Hello everyone.

I have a discrete system, a sampling interval is 0.1 sec, including a sliding mode control with A, B, C, D matrices and I want to get a gain matrics, but I cannot figure out how to calculate optimum Q,R matrices and an Epsilon number.

I would be really thankful if anybody could check out my code and tell me how to find Q,R matrices and an Epsilon number and get a desired response.

Thank you.

A=[0.4658   -0.5236         0
   0.5000         0         0
   0         0.5000         0];
B=[0.2500
   0
   0];
C=[0.0093    0.2214   -0.1554];
D=0.4152;

[n,m] = size(B);
[p,n] = size(C);

Q=[? ? ? ?];
R=?;
Epsilon=?;

Ao = [zeros(p) -C;zeros(n,p) A];
Bo = [zeros(p,m);B];
Eo = [eye(p);zeros(n,p)];

AEo = Ao+Epsilon*eye(n+p);
Qo = diag(Q);
Ro = R*eye(m);

S = dlqr(AEo,Bo,Qo,Ro);      % S: gain matrics
SA = S*Ao;
SE = S*Eo;
INVSB = inv(S*Bo);

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