Most LMIs and H-infinity controllers require an iterative search to solve the controller problem. I am guessing that you would like to solve the problem within a hard deadline for some real-time application? If so you can use the normalized coprime factorization H-infinity approach of Glover and Macfarlane. The MATLAB solution does use iteration, but there is a non-iterative solution (suggested I think by Safanov). I have used it for a similar reason. If this is what you are looking for, let me know & I will post the references.
I think that system identification by step change, then MATLAB simulation before implementation greatly reduced the mathematical difficulties in any control strategy