Problems with nested MATLAB statements and halving

New to the site, but I'm trying to hone some MATLAB skills for work and study and was looking for some help with the following:

I want to write my own algorithm for finding the Hinf norm of a system using halving, as the MATLAB function 'hinfsyn' does.

I have included the code that I have so far:

function [ hnorm ] = matmath(A,B,C,D,glow,ghigh,tol)

if 2*(ghigh-glow) < tol
    gam  = (ghigh+glow)/2;
    hnorm = gam;
else
    Dgam = ((gam^2)*eye(size(D)))-(D'*D);
    A_clp = [ A + (B/Dgam*D'*C) -B/Dgam*B'
        (C'*C) + C'*D/Dgam*D'*C -A'-(C'*D/Dgam*B')];
    eigcl = eig(A_clp);
    for i = 1:length(eigcl)
        if real(eig(i)) == 0
            glow = gam;
        else
            ghigh = gam;
        end
    end
end

      

        
        
        
      

    

I rationalized the problem into a few steps:

• Using the gamma bounds as input, compute the first iteration: gam = (ghigh-glow) / 2. If 2 * (ghigh-glow) <tol then the program stops with hinf = gam.
• Compute the eignvalues ​​of the closed loop matrix A.
• Check purely imaginary eigenvalues. If there is a purely imaginary eigenvalue, then the new glow = gam. Otherwise set ghigh = gam.
• Keep repeating until you are satisfied with the gamma accuracy.

I believe my calculations in the matrix are correct, but I have a hard time working with if / for statements. My code only completes the first iteration when I run it in MATLAB. Any advice would be greatly appreciated! Thank!

Update: Here is the code I have simplified that completes one iteration successfully and has been tested for different values.

function [ hnorm ] = matmath(A,B,C,D,glow,ghigh,tol)

gam  = (ghigh+glow)/2;

if 2*(ghigh-glow) < tol
    hnorm = gam
else    

Dgam = ((gam^2)*eye(size(D)))-(D'*D);
A_clp = [ A + (B/Dgam*D'*C) -B/Dgam*B'
        (C'*C) + C'*D/Dgam*D'*C -A'-(C'*D/Dgam*B')];
eig_clp = eig(A_clp)

for z = 1:length(eig_clp)
    if abs(real(eig_clp(z)))<1e-10
        glow = gam
        break
    end
end

ghigh = gam

end