Many problems in systems and control can be formulated as follows (see [2])
where
are unknown real matrices, referred to as the
unknown matrices,
; it is referred to as the objective function,
's are real matrices with entries which are affine functions of the
entries of the unknown matrices, ;
they are referred to as ``Linear Matrix Equality'' (LME) functions,
's are real symmetric matrices with entries which are affine functions
of the entries of the unknown matrices ; they are referred to as
``Linear Matrix Inequality'' (LMI) functions. (In this report,
the 
stands for V positive semi-definite unless stated otherwise).
in a user-friendly manner
in Scilab, using the code SP [1].
This code is intended for
small and medium-sized problems (say, up to a few hundred variables).