Asymptotic stability of 2-D positive linear systems with orthogonal initial states

作者：Zhu Qiao^*; Cui Jia Rui; Hu Guang Da

来源：Acta Automatica Sinica, 2013, 39(9): 1543-1546.

DOI：10.3724/SP.J.1004.2013.01543

• 2-D systems
• Fornasini-Marchesini model
• Initial state
• Positive linear systems
• Roesser models

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) (FornasiniMarchesini (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.

• 出版日期2013
• 单位北京科技大学