在本論文中，首先針對多輸出多輸入的線性系統，提出一個公式來設計積分型可變結構控制器，這個公式是基於互質矩陣分式表示來發展設計積分型滑動平面和可變結構控制器，所提的方法不僅避免需要轉換型式，而且能夠使要設計的系統能有想要的性能。
然後接著我們針對T-S模糊系統基於李亞普若夫函數來設計模糊可變結構控制器，此方法並不需要假設每個子系統的輸入矩陣是相同的，並顯示了李亞普若夫函數可以被用來建立模糊滑動平面藉著解出一組雙線性矩陣不等式，我們提出一個反覆迭代的線性矩陣不等式演算法來解決雙線性矩陣不等式的問題，並且我們針對T-S模糊時間延遲系統基於模糊李亞普若夫函數來設計模糊可變結構控制器，並顯示了模糊李亞普若夫函數也可以被用來建立模糊滑動平面藉著解出一組雙線性矩陣不等式，我們提出另一個演算法來解決雙線性矩陣不等式的問題。

In this thesis, we present an approach to design an integral variable structure controller for linear multi-input/multi-output (MIMO) systems. A closed-form formula based on the coprime matrix fraction description (MFD) is developed to solve integral sliding surface for a class of linear MIMO systems and the control function is determined. The proposed method not only avoids transforming the original plant into a companion form, but also enables the designed system to exhibit the desired dynamic properties. Then, we design a variable structure controller for the T-S fuzzy systems based on the Lyapunov function. It is not necessary to assume that each local system shares the same input matrix. It is shown that the Lyapunov function can be used to establish a sliding surface by solving a set of bilinear matrix inequalities (BMIs). We propose an iterative linear matrix inequality (ILMI) algorithm to solve the BMIs problem. Moreover, we design a variable structure controller for the T-S fuzzy time-delay systems based on a fuzzy Lyapunov function. It is also shown that the fuzzy Lyapunov function can be used to establish a sliding surface by solving a set of bilinear matrix inequalities (BMIs). We also propose alternative algorithm to solve the corresponding BMIs problem. Furthermore, it is shown that the proposed scheme ensures the trajectory of the system under the variable structure control can reach the sliding surface and stay on it thereafter. And we show that the motion of the system on the sliding surface is asymptotically stable.

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