切換式系統實際可穩定之高階穩定條件之研究

Abstract

本論文主要主題為探討切換系統實際可穩定之相關問題，本論文中，我們首先回顧了一些實際可穩定的相關定義，接著陳述研究實際穩定性之動機，最後推導出對於任何非線性切換系統實際可穩定的充分條件以及切換律要如何選取。而接下來的主題是有關於可控性在切換系統上的研究，包含一些切換系統上可控的定義、可控的充分條件、以及切換法則與控制律要如何選取，最後並歸納出一套設計切換法則與控制律的演算法則。

Issues regarding practical stabilizability of a class of nonlinear switched systems and controllability of switched linear systems are addressed in this thesis. To avoid possible chattering behavior, a high-order sufficient condition and its associated algorithm for achieving practical stabilizability are proposed. It is shown that, under the designed switching law, the state is convergent to a neighborhood of the origin with pre-specified accuracy, while greatly alleviating the chattering phenomenon. On the other hand, this thesis also recalls some of the checking conditions for controllability of switched linear systems, and presents an algorithm to implement the checking condition and the state transfer tasks. Examples demonstrate the usage and the benefits of these approaches.