Decentralized Stabilization of Infinite Networks of Systems with Nonlinear Dynamics and Uncontrollable Linearization

Abstract

We solve the problem of decentralized uniform stabilization for infinite networks of lower-triangular form systems with uncontrollable linearization. Since the network is composed of a countable set of agents, we revise the framework of small gain theorems accordingly. We prove a new small gain theorem and use it as a tool in our design of decentralized stabilizers. Then we construct a feedback for each individual agent to provide a suitable gain assignment and to satisfy the conditions of our new small gain theorem. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case.