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The aim of this short communique is to adapt a result established by Bliman,related to the possible approximation of the solutions toreal-parameter-dependent linear matrix inequalities (LMIs), to the specialcontext of stability analysis of 2D discrete Roesser models. While Blimanconsidered the case of LMIs involving several real parameters, which isespecially crucial for the analysis of linear systems against parametricdeflections, the stability of Roesser models leads to consider LMIs with onlyone single complex parameter. Extending the results from real parameters tocomplex ones is not straightforward in our opinion. This is why the presentnote discusses precautions to be taken concerning this case before applying theresults in a 2D context. Actually, it is shown that a well-known condition forstructural stability of a 2D discrete Roesser can be relaxed into an LMI systemwhose solution polynomially depends on a single complex parameter over the unitcircle.

On the solutions to complex parameter-dependent LMIs involved in the stability analysis of 2D discrete models