On new sufficient conditions for stability of switched linear systems

This work aims to connect two existing approaches to stability analysis of switched linear systems: stability conditions based on commutation relations between the subsystems and stability conditions of the slow-switching type. The proposed sufficient conditions for stability have an interpretation in terms of commutation relations; at the same time, they involve only elementary computations of matrix products and induced norms, and possess robustness to small perturbations of the subsystem matrices. These conditions are also related to slow switching, in the sense that they rely on the knowledge of how slow the switching should be to guarantee stability; however, they cover situations where the switching is actually not slow enough, by accounting for relations between the subsystems. Numerical examples are included for illustration.