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摘要: 本文分析了初始状态为正交的二维线性正系统的渐近稳定性. 与一维系统不同, 初始状态为正交的二维系统的稳定性严格依赖于合适的初始条件. 首先, 当初始状态 绝对收敛时, 二维正FM I 模型的渐近稳定性判据被提出. 然后, 针对二维正Rosser模型, 在初始状态 绝对收敛时, 相似的结论被给出. 最后, 两个数字实例证实了这些判据的有效性.Abstract: 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,i) (Fornasini-Marchesini (FM) model) or xv(i,0), xh(0,i) (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,i) 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,i). 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.
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