A note on applications of a trajectory-based small-gain theorem to decentralized stabilization of switching networks with generalized dead zones

We propose a method for uniform decentralized stabilitzation for a class of large-scale networks of nonlinear switched systems in lower-triangular form with unknown arbitrary switchings. In contrast to the class of networks with the same structure of interconnections that was considered in [1], the dynamics of each subsystem of our network satisfies more general conditions and its input–output maps are not necessarily right invertible, for instance, they can have dead zones. Another difference from [1] is that the current result is proved by a different approach. Instead of using a small-gain theorem in terms of ISS Lyapunov functions as in [1], we use the trajectory-based small-gain theorem for switched systems proved in [2].