Before revision:  Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, and thereby ensures exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances.
After revision:  Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances.