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This paper proposes the design of two coordinated wide-area damping controllers (CWADCs) for damping low frequency oscillations (LFOs), while accounting for the uncertainties present in the power system. The controllers based on Deep Neural Network (DNN) and Deep Reinforcement Learning (DRL), respectively, coordinate the operation of different local damping controls such as power system stabilizers (PSSs), static VAr compensators (SVCs), and supplementary damping controllers for DC lines (DC-SDCs). The DNN-CWADC learns to make control decisions using supervised learning; the training dataset consisting of polytopic controllers designed with the help of linear matrix inequality (LMI)-based mixed $H_2/H_\infty$ optimization. The DRL-CWADC learns to adapt to the system uncertainties based on its continuous interaction with the power system environment by employing an advanced version of the state-of-the-art deep deterministic policy gradient (DDPG) algorithm referred to as bounded exploratory control-based DDPG (BEC-DDPG). The studies performed on a 33 machine, 127 bus equivalent model of the Western Electricity Coordinating Council (WECC) system-embedded with different types of damping controls demonstrate the effectiveness of the proposed CWADCs. [ABSTRACT FROM AUTHOR]