This paper analyzes distributed control protocols for first- and second-order
networked dynamical systems. We propose a class of nonlinear consensus
controllers where the input of each agent can be written as a product of a
nonlinear gain, and a sum of nonlinear interaction functions. By using integral
Lyapunov functions, we prove the stability of the proposed control protocols,
and explicitly characterize the equilibrium set. We also propose a distributed
proportional-integral (PI) controller for networked dynamical systems. The PI
controllers successfully attenuate constant disturbances in the network. We
prove that agents with single-integrator dynamics are stable for any integral
gain, and give an explicit tight upper bound on the integral gain for when the
system is stable for agents with double-integrator dynamics. Throughout the
paper we highlight some possible applications of the proposed controllers by
realistic simulations of autonomous satellites, power systems and building
temperature control.

分析了用于网络动力系统的分布式控制协议，提出了一类非线性共识控制器；并通过使用积分李雅普诺夫函数证明了所提出的控制协议的稳定性，同时明确表述了均衡集；之后又提出了分布式比例积分控制器，用于网络动力系统的稳定；通过在自主卫星，电源系统和建筑温度控制的实际模拟中突出了所提出的控制器的一些可能的应用。