Exponential convergence under distributed averaging integral frequency   control
  We investigate the performance and robustness of distributed averaging integral controllers used in the optimal frequency regulation of power networks. We construct a strict Lyapunov function that allows us to quantify the exponential convergence rate of the closed-loop system. As an application, we study the stability of the system in the presence of disruptions to the controllers' communication network, and investigate how the convergence rate is affected by these disruptions. 
Erik Weitenberg, Claudio De Persis, Nima Monshizadeh
math.OC cs.SY