Asymptotic Stability of 2-D Positive Linear Systems with Orthogonal Initial States

This paper deals with the asymptotic stability of 2-D positive linear systems with orthogonal initial states. Different from the 1-D systems, the asymptotic stability of 2-D systems with orthogonal initial states x(i, 0), x(0, j) (Fornasini-Marchesini (FM) model) or xv (i, 0), xh (0, j) (Roesser model) is strictly dependent on proper boundary conditions. Firstly, an asymptotic stability criterion for 2-D positive FM first model is presented by making initial states x(i, 0), x(0, j) absolutely convergent. Then, a similar result is also given for 2-D positive Roesser model with any absolutely convergent initial states xv (i, 0), xh (0, j). Finally, two examples are given to show the effectiveness of these criteria and to demonstrate the convergence of the trajectories by making exponentially convergent initial states.