Dynamic statistical linearization

The problem of linearization is defined as the approximation of a nonlinear system by a general dynamic linear operator which is defined over the class of the system input functions. From this standpoint, the concept of dynamic statistical linearization is developed. The approach is formulated in a general way for the nonstationary nonlinear case, and the necessary and sufficient conditions are presented for the specification of an optimal equivalent-linear system. A mean-square error criterion is used to develop a modified Wiener-Hopf equation, with explicit solutions being obtained for systems subject to stationary random inputs, and for systems subject to deterministic functions of random amplitude.