  The aim of this short communique is to adapt a result established by Bliman,
related to the possible approximation of the solutions to
real-parameter-dependent linear matrix inequalities (LMIs), to the special
context of stability analysis of 2D discrete Roesser models. While Bliman
considered the case of LMIs involving several real parameters, which is
especially crucial for the analysis of linear systems against parametric
deflections, the stability of Roesser models leads to consider LMIs with only
one single complex parameter. Extending the results from real parameters to
complex ones is not straightforward in our opinion. This is why the present
note discusses precautions to be taken concerning this case before applying the
results in a 2D context. Actually, it is shown that a well-known condition for
structural stability of a 2D discrete Roesser can be relaxed into an LMI system
whose solution polynomially depends on a single complex parameter over the unit
circle.
