This study takes advantage of wide area measurements to propose a centralized nonlinear controller that acts on power system stabilizers, to cooperatively increase the damping of problematic small signal oscillations all over the system. The structure based on decision trees results in a simple, efficient, and dependable methodology that imposes much less computational burden than other nonlinear design approaches, making it a promising candidate for actual implementation by utilities and system operators. Details are given to utilize existing stabilizers while causing minimum changes to the equipment, and warranting improvement or at least no detriment of current system behavior. This enables power system stabilizers to overcome their inherent limitation to act only on the basis of local measurements to damp a single target frequency. This study demonstrates the implications of this new input on mathematical models, and the control functionality that is made available by its incorporation to conventional stabilizers. In preparation of the case of study, a heuristic dynamic reduction methodology is introduced that preserves a physical equivalent model, and that can be interpreted by any commercial software package. The steps of this method are general, versatile, and of easy adaptation to any particular power system model, with the aggregated value of producing a physical model as final result, that makes the approach appealing for industry. The accuracy of the resulting reduced network has been demonstrated with the model of the Central American System. / Ph. D.