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THE ANALYSIS of nonlinear control systems is not a new problem. In 1918, Barbillion1,2 investigated the use of a hydraulic servomotor in a nonlinear regulating control system. The work of Babillion and Cayere is a modification of the principle given by Leaute' in 1885 in his treatise on the prevention of long period oscillations in machines driven by water turbines. In considering the operation of the servomotor, Leaute' suggested that the servomotor should be advanced to damp out the oscillations in question. In all cases there is more or less considerable oscillation of speed and the regulation is made by successive approximations.