Observer and controller design for a nonlinear system has been studied in the automatic control field for decades. However, if the nonlinear system is affected by the disturbance or/and uncertainty, this design work becomes much more difficult. In this talk, we will introduce the observer or/and controller synthesis for the uncertain nonlinear system which is represented as the T-S fuzzy system model, polynomial system model, and polynomial fuzzy system model, respectively. In these models, the exact form and the upper bound of the uncertainty can be unknown. Based on the unknown input method, the effect of the uncertainty or disturbance will be eliminated. Simultaneously, the observer can be synthesized with some conditions being satisfied. Furthermore, we also introduce the observer based controller synthesis for the uncertain polynomial system. In the study, the un-measurable states are estimated and the stability of the system is guaranteed. To deal with the above problems, the non-common quadratic Lyapunov function, Linear Matrix Inequality (LMI) technique, and Sum-of-Square (SOS) technique are used to derive the sufficient conditions for the observer and controller synthesis for the uncertain nonlinear system.