  We study the problem of mean-square exponential incremental stabilization of
nonlinear systems over uncertain communication channels. We show the ability to
stabilize a system over such channels is fundamentally limited and the channel
uncertainty must provide a minimal Quality of Service (QoS) to support
stabilization. The smallest QoS necessary for stabilization is shown as a
function of the positive Lyapunov exponents of uncontrolled nonlinear systems.
The positive Lyapunov exponent is a measure of dynamical complexity and
captures the rate of exponential divergence of nearby system trajectories. One
of the main highlights of our results is the role played by nonequilibrium
dynamics to determine the limitation for incremental stabilization over
networks with uncertainty.
