Abstract
We prove a new theorem on ℓ∞-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 ℓ∞-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.
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