The Discrepancy from the Normal Distribution of the Probability of the Response of Nonlinear Control Systems Subjected to a Gaussian Random Input

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In this paper, the discrepancy from the normal distribution of the response of nonlinear control systems excited by a stationary Gaussian signal is quantitatively discussed by evaluating the skewness, β1, and the kurtosis, β2, for the probability distribution of response. The approach is carried out by introducing the theory of a Markov process and solving the Fokker-Planck equation. Nonlinear characteristic considered here is a symmetric one. The discussion is, therefore, directed to the evaluation of the kurtosis, β2, as function of the various values of nonlinearity. The remainder of this paper is devoted to justify the previous consideration as already presented by the authors that the response has the same amplitude distribution function as the system input. For this purpose, a new quantity, the confidence, is defined. As a result, the dependency of nonlin-earity in the system on the probability distribution of response is obtained and the confidence that the probability distribution function can be regarded as the normal one is also evaluated by numerical computations.