Control of a nonlinear static MIMO System

Based on your comment, it seems like you are trying to control a dynamical system to track some reference trajectory subject to Gaussian disturbances. Suppose you have some kind of model for the dynamics, then the discrete system can be written as

$$ begin{align} x_{k+1} &= f_k(x_k) + a_k w_k y_k &= x_k end{align} $$

where $w_k$ is a Gaussian vector with mean $mu_k = [x_a^{(k)}, y_a^{(k)}]^intercal$ and covariance $Sigma_{x_k} = frac{b^{(k)}}{2} I_2$. This is then a stochastic Control problem and there are various methods to create a stabilizing controller just check out the literature.

I think there are many systems similar to your system.

A very common way to write a system with a nonlinearty is by writing it as Luré Type System, where the nonlinearity is in the feedback loop $$ begin{align} dot{x}(t) &= Ax(t) +Bw(t) z(t) &= Cx + Dw(t) w(t) &= Delta(t,z) end{align}$$ where $Delta$ is the nonlinearty.

Depending on the type of nonlinearty, you can apply all kinds of controller synthesis such as $H_infty$, $H_2$ and QP.

For example, you can create a sector condition for the nonlinearty and use the Circle Criterion to check if the system is absolutely stable. A common nonlinearty to use in this framework is a saturation.