A study of nonlinear systems with random inputs

IT IS THE PURPOSE of this paper to present the results of investigating the probability distribution of the response of a nonlinear system when it is subjected to a Gaussian random input. The mathematical theory of a Markoff random process is used; the associated Fokker-Planck equation for a generalized continuous nonlinear system is presented. The justification for assuming the error response of a nonlinear control system as being a Markoff process is discussed.