The authors consider the system with saturating actuators, having the state-space representation \[ \dot x_G=Ax_G+B_1w+B_2 \varphi(u),\quad z=C_1x_G+D_{12}u,\quad y=C_2x_G+D_{21}w, \] where \(x_G=[x_P^T, x_A^T, x_{F_1}^T, x_{F_2}^T, x_{H_1}^T , x_{H_2}^T]^T\in\mathbb R^{n_G}\), \(w=[w_1, w_2]^T\), \(z=[z_1, z_2]^T\), \(\varphi(u)\) is the static saturation nonlinearity, \(\varphi(u)=\beta\text{ sat}(u/\alpha)\), \(\alpha>0\), \(\beta>0,\) \(A(s)\) describes the dynamics of the actuator, \(C(s)\) is the controller, \(P(s)\) is the plant, \(F_1(s), F_2(s)\) are coloring filters, and \(H_1(s),H_2(s)\) are weighting filters. Signals \(u,y\in\mathbb R\) are the commanded control, and measured output, respectively, \(w_1,w_2\in\mathbb R\) are standard uncorrelated white noise processes, and \(z_1,z_2\in\mathbb R\) are the controlled outputs. The authors are interested in the steady-state variance \(\sigma_z^2\) of \(z\) and address the problem: Find a controller \(C(s)\) that stabilizes the system when \(w=0\) and minimizes \(\sigma_z^2.\) An extension of the LQR/LQG methodology to this system, referred to as SLQR/SLQG, is obtained, where the S stands for ``saturating''. The development is based on the method of stochastic linearization. Using this method and the Lagrange multiplier technique, a solution to the SLQR/SLQG problem is derived. This solution is given by the standard Riccati equations coupled with two transcendental equations, which define the variance of the signal at the input of the saturation and the Lagrange multiplier associated with the quadratic performance index. It is shown that, under the standard stabilizability and detectabitity conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the saturation is removed, these equations reduce to the standard LQR/LQG solution.