Towards LMI necessary and sufficient stability conditions for 2D Roesser models

This article is devoted to the stability analysis of linear two-dimensional systems described by Roesser models. The models can be discrete, continuous, or mixed continuous-discrete. The same formalism is used for the three cases. The S-procedure is used to relax commonly used polynomial-based tests of stability. As a result, stability tests of the Roesser models are reduced to that of checking the existence of a solution constrained by a set of linear matrix inequalities, an attractive result from a computational point of view. Therefore, the approach is very general and it is also shown that under certain conditions the provided results are not only sufficient but also necessary.