Distributed PID Control for Consensus of Homogeneous and Heterogeneous   Networks
  We investigate the use of distributed PID actions to achieve consensus in networks of homogeneous and heterogeneous linear systems. Convergence of the strategy is proved for both cases using appropriate state transformations and Lyapunov functions. The effectiveness of the theoretical results is illustrated via its application to a representative power grid model recently presented in the literature. 
Daniel Burbano and Mario di Bernardo
math.OC