Decentralized uniform input-to-state stabilization of hierarchically interconnected triangular switched systems with arbitrary switchings

We consider a class of large-scale systems composed of hierarchically interconnected switched nonlinear triangular form subsystems affected by external disturbances with arbitrarily varying switching signals. For any system of this class, we design a decentralized feedback controller which renders the entire large-scale closed-loop system globally ISS with respect to the external disturbances uniformly and regardless of the unknown switching signals. To solve the problem, we use a certain modification of the classical small gain theorems formulated in terms of the ISS Lyapunov functions and combine it with our version of the backstepping approach with a suitable gain assignment.