This paper derives necessary and sufficient (N&S) conditions for the exponential stability of discrete-time switched positive linear systems under transfer-restricted switching. The transfer-restricted switching property is characterized by a switching digraph, and the structural properties for subsystems are characterized by a novel class of state component digraphs. Combining with the two properties, some joint path conditions involving the sum and product matrices of multiple subsystems respectively are presented as N&S conditions based on weak common linear co-positive Lyapunov functions (weak-CLCLFs). The presented conditions allow all subsystems to be marginally stable rather than asymptotically stable. Finally, a simulation example is provided to show the effectiveness and superiority of the proposed method.

中文翻译：

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基于图的 Switchpositive Systems 的指数稳定性的必要和充分条件，具有边际稳定的子系统


本文推导出了转移限制开关下离散时间开关正线性系统指数稳定性的必要和充分 （N&S） 条件。传输限制开关属性以开关有向图为特征，子系统的结构属性以一类新型状态分量有向图为特征。结合这两个性质，将一些分别涉及多个子系统的和矩阵和乘积矩阵的联合路径条件表示为基于弱共同线性共正 Lyapunov 函数 （weak-CLCLFs） 的 N&S 条件。所提出的条件允许所有子系统都是边际稳定的，而不是渐近稳定的。最后，通过仿真算例验证了所提方法的有效性和优越性。