Stability of 2D Roesser models: Towards a necessary and sufficient LMI condition

This paper is dedicated to the asymptotic stability of 2D discrete Roesser models. Two well-known necesssary and sufficient conditions expressed in terms of characteristic polymials are recalled and their equivalence is proved. Although it is not new result, the provided proof is simpler than those proposed in the literature. These conditions being numerically rather non tractable, a first motivation is to compare these conditions through their sufficient LMI (Linear Matrix Inequalities) relaxations. Actually, the same approach, based upon the S-procedure, is used to derive the two relaxations, which, once again, are proved to be equivalent. However, the second condition offers a different point of view which leads to a modification of the relaxation technique, making the necessity of the LMI condition reachable.