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

Conference: nDS '13 - Proceedings of the 8th International Workshop on Multidimensional Systems
09/09/2013 - 09/11/2013 at Erlangen, Deutschland

Proceedings: nDS '13

Pages: 6Language: englishTyp: PDF

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Authors:
Bachelier, Olivier; Yeganefar, Nima; Mehdi, Driss (University of Poitiers, LIAS-ENSIP, Bâtiment B25, 2 rue Pierre Brousse, B.P. 633, 86022 Poitiers Cedex, France)
Paszke, Wojciech (University of Zielona Gora, Institute of Control and Computation Engineering, ul. Licealna 9,65-417 Zielona Gora, Poland)

Abstract:
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.