Decentralized fixed-time uniform ISS stabilization of infinite networks of switched nonlinear systems with arbitrary switchings by small gain approach

We prove a new theorem on ${\ell }_{\infty }$-fixed-time uniform ISS decentralized stabilization of infinite networks composed of interconnected switched nonlinear systems with unknown switching signals. Each subsystem has the lower-triangular form with uncontrollable linearization, more specifically, it has the lower-triangular form with the so-called “generalized polynomial integrators”. To solve this problem, we use a new small gain theorem on ${\ell }_{\infty }$-fixed-time uniform input-to-state stability of infinite networks and redesign several previous backstepping algorithms of decentralized stabilization. In particular, our main result generalizes several recent related ones.