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Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper, we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed- averaging-based integral control in theory and simulations. 

We investigate the robustness of the so-called leaky integral frequency controller for the power network. In particular, using a strict Lyapunov function, we show the closed-loop system is robust in the input-to-state stability sense to measurement noise in the controller. Moreover, an interesting and explicit trade-o between controller performance and robustness is discussed and illustrated using a bench- mark study of the 39-bus New England reference network.