Graph-based necessary and sufficient conditions for exponential stability of switched positive systems with marginally stable subsystems

This paper derives necessary and sufficient (N&S) conditions for the exponential stability of discretetime 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. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.