The LMI Lab can handle any system of LMIs of the form
NT L(X1, . . . , XK) N < MT R(X1, . . . , XK) M
X1, . . . , XK are matrix variables with some prescribed structure
The left and right outer factors N and M are given matrices with identical dimensions
The left and right inner factors L(.) and R(.) are symmetric block matrices with identical block structures, each block being an affine combination of X1, . . . , XK and their transposes.
The specification of an LMI system involves two steps:
This process creates the so-called internal representation of the LMI system. This computer description of the problem is used by the LMI solvers and in all subsequent manipulations of the LMI system. It is stored as a single vector called LMISYS.
There are two ways of generating the internal description of a given LMI system: (1) by a sequence of lmivar/lmiterm commands that build it incrementally, or (2) via the LMI Editor lmiedit where LMIs can be specified directly as symbolic matrix expressions. Though somewhat less flexible and powerful than the command-based description, the LMI Editor is more straightforward to use, hence particularly well-suited for beginners. Thanks to its coding and decoding capabilities, it also constitutes a good tutorial introduction to lmivar and lmiterm. Accordingly, beginners may elect to skip the subsections on lmivar and lmiterm and to concentrate on the GUI-based specification of LMIs with lmiedit.