A New Cycle-Node Commutator Approach for Stability Analysis of Switched Systems With Transfer-Restricted Switching

This brief proposes a new approach to addressing the global exponential stability (GES) of switched systems with all unstable subsystems under transfer-restricted switching. The switching digraph is used to describe the transfer relationship between subsystems. A novel cycle-node commutator approach is proposed to rearrange all possible switching paths obtained under the switching digraph. Then, sufficient conditions for the GES of switched systems are established in the form of scalar inequalities. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.