Stabilization of nonlinear systems over packet-drop links: Scalar case

In this paper, we study the stabilization problem of a scalar nonlinear system over a packet-drop channel. We consider moment stability notions adopted from the ergodic theory of dynamical systems. The main result of this paper proves that qq-moment exponential stability requires a minimal quality of service from the communications link. The necessary conditions presented in the paper relate the positive Lyapunov exponent of the open loop system and the largest probability of erasure. For the first time, the dependence on the Lyapunov exponent highlights the important role played by the global non-equilibrium dynamics in nonlinear stabilization over networks.