  Stochastic linearization is a method used in Quasilinear Control (QLC) to
replace a nonlinearity by an equivalent gain and a bias, utilizing the
statistical properties of random inputs. In this paper, the theory of
stochastic linearization is extended to nonlinear functions of multiple
variables or inputs forming a multivariate Gaussian vector. The result is
applied to find the stochastic linearization of a bivariate saturation
nonlinearity in a general feedback control system. The accuracy of stochastic
linearization has been investigated by a Monte Carlo simulation and has been
found out to be fairly high. Finally, a practical example of optimal control
design using QLC is presented.
