  Uncertainty from renewable energy and loads is one of the major challenges
for stable grid operation. Various approaches have been explored to remedy
these uncertainties. In this paper, we design centralized or decentralized
state-feedback controllers for generators while considering worst-case
uncertainty. Specifically, this paper introduces the notion of
$\mathcal{L}_{\infty}$ robust control and stability for uncertain power
networks. Uncertain and nonlinear differential algebraic equation model of the
network is presented. The model includes unknown disturbances from renewables
and loads. Given an operating point, the linearized state-space presentation is
given. Then, the notion of $\mathcal{L}_{\infty}$ robust control and stability
is discussed, resulting in a nonconvex optimization routine that yields a state
feedback gain mitigating the impact of disturbances. The developed routine
includes explicit input-bound constraints on generators' inputs and a measure
of the worst-case disturbance. The feedback control architecture can be
centralized, distributed, or decentralized. Algorithms based on successive
convex approximations are then given to address the nonconvexity. Case studies
are presented showcasing the performance of the $\mathcal{L}_{\infty}$
controllers in comparison with automatic generation control and
$\mathcal{H}_{\infty}$ control methods.
