In this paper, we consider a class of nonlinear regulator problems in which the control appears linearly. Using an approach similar to that given for the classical linear quadratic regulator problem, it is shown in  that the optimal feedback control can be expressed as a function of the solution of an algebraic Riccati equation at each point in the state space. More precisely, it is shown that by solving a Riccati equation at a given point in the state space, the optimal feedback control at that particular point is readily obtained. In this paper, our first aim is to investigate stability of the resulting closed loop system. Second, a simple computational scheme for constructing a suboptimal control is suggested. We then consider the problem of stabilizing the system when it is subjected to bounded noise. For illustration, two examples are used to test the effectiveness of the proposed computational schemes.
Teo, K. L., Rehbock, V., & Jennings, L. (1996). Optimal and suboptimal feedback controls for a class of nonlinear systems. Computers & Mathematics with Applications, 31, 71 - 89. https://doi.org/10.1016/0898-1221(96)00007-7