Stability of one-dimensioned spatially interconnected systems

This article is dedicated to the stability of one-dimensioned spatially interconnected systems. More precisely, it focuses on systems which results of the interconnection of a possibly large number of cells (continuous subsystems). This note is restricted to the case where cells are just distributed along a line. The global system can then be seen as a mixed continuous–discrete 2D Roesser system but with implicit discrete dynamics along the space dimension. Recent results on the stability of 2D Roesser models are exploited and adapted to derive a sufficient condition for such a system to be stable. The condition seems to be close to necessity if not necessary. It is tractable since it is expressed in terms of linear matrix inequalities. The novelty clearly lies in the reduction of the conservatism of the proposed analysis.