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An LMI approach to checking stability of 2D positive systems

Twardy M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 4

385-395

Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both Fornasini-Marchesini models (FF-MM and SF-MM) and for the general model.