I would like to solve the following LMI optimization problem in matrices Y and L with MATLAB. What MATLAB function should be used for solving the LMI problem? I don't know how I can define system of LMIs? I was wondering if anyone could help me with it. Thank you in advance.
This is a Semi-Definite Program (SDP). By definition it is a convex problem. To this date, the best Matlab package to setup this class of optimization problems is YALMIP. YALMIP provides an interface for most of the well-known SDP solvers such as SeDuMi, SDPT3 and SDPA. For a quick guide on how to set-up SDPs in YALMIP take a look at:
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Basics
and
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.SemidefiniteProgramming
Here is a link to download SeDuMi:
http://sedumi.ie.lehigh.edu/downloads
Alternatively, you can use the LMILab package. It is a built-in Matlab package which uses an obsolete SDP solver, but still good enough to solve your problem if the size of the matrix variables Y and L is not too large.
I think you need the Robust Control Tool Box to solve this LMI problem
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