Quasilinear Control (QLC) is a set of methods for analyzing and designing nonlinear stochastic systems. It leverages the method of Stochastic Linearization (SL), which approximates a nonlinearity by a linear function, utilizing statistical properties of the random inputs. In this paper, the theory of multivariable SL is studied, leading to a multivariable extension of QLC theory. The expression for the linear function is derived in terms of the inputs to the nonlinearity. The expression is then used to stochastically linearize a bivariate saturation nonlinearity in a feedback control system. Finally, a practical example of optimal control design is presented, where it is shown that SL is fairly accurate even for multivariate nonlinearities and that the resulting linear approximation can adapt systematically to changes in system parameters.
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