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In this paper, artificial neural network (ANN) and simulated annealing (SA) techniques are combined with Hinfin-control theory to design two adaptively robust output feedback controllers. The first controller, robust Hinfin controller (RHC), is based on the of the Hinfin-norm of disturbance-to-output transfer function using linear matrix inequalities technique. The second one, robust lead-lag (RLL), is a lead-lag type of controller whose optimum parameters are found using the optimization of an Hinfin-norm via simulated annealing. The former is characterized by similar size as the plant that may be of higher order and thus creates difficulty in implementation in large systems. The later is shown to be robust and more appealing from an implementation point of view since its size is lower. Artificial neural network (ANN) is used to make the control setting gains adaptive to change in the operating conditions. Both controllers and the conventional lead-lag (CLL), added for comparison purposes, are used as power system stabilizer for a single-machine infinite-bus sample power system. The proposed controllers show to present robustness over a wide range of operating conditions and parameters change.