在本論文中，我們針對離散Takagi-Sugeno (T-S) 模糊系統設計模糊觀測器來估測系統的狀態值。因為T-S 模糊模型與非線性系統特性相似，所以我們用T-S 模糊模型來表示非線性系統。根據平行分佈補償的方法，可使用線性之回授增益來驅動非線性隨機系統。針對離散時間T-S 模糊系統的穩定性分析，我們利用Lyapunov穩定法則以及兩步驟的線性矩陣不等式演算法。並且考慮了系統外部雜訊(Disturbance)干擾和多重雜訊(Multiple Noises)的干擾，當系統遭受外來干擾影響時，設計模糊控制器以使系統之H∞ 效能亦能被保證。本文最後舉出非線性模型車的系統模擬來驗證本篇論文所提理論之可行性。 This thesis discusses a class of discrete-time observer-based nonlinear stochastic systems, which are modeled by the Takagi-Sugeno (T-S) fuzzy models. Because of the dynamic properties of T-S fuzzy model and nonlinear system are similar; hence, we can represent the nonlinear systems by T-S fuzzy models. According to Parallel Distributed Compensation (PDC) concept, the nonlinear stochastic systems can be driven by the linear feedback gains. Through the Lyapunov stability criterion and two-step Linear Matrix Inequality (LMI) algorithm, the stability analysis and observer-based fuzzy controller design of discrete time stochastic T-S fuzzy system are discussed in this thesis. Moreover, the external disturbance is also considered into the controller design procedure for discrete-time stochastic T-S fuzzy system. The H∞ control technique is applied to deal with the control problem that the H∞ performance is guaranteed for the worst case effect of disturbance on system states. Finally, some numerical examples are provided to verify the effects of the proposed approach.