兩個不穩定線性系統存在穩定切換律之探討與應用

Abstract

本論文主要是針對於二階與n階不穩定系統間是否存在利用里奧波諾夫分析方法建構出切換律使不穩定狀態系統藉由切換達到穩定之目的，並且證明已經存在的三個充分的條件是互相對等的；接著我們把利用里奧波諾夫分析方法建構切換律的適用條件推廣到擁有輸入的不可穩定狀態的控制系統中，並且提出一個尋找切換律使得此包含有控制律的n階不穩定系統達到穩定的方法，以及建立出使用此方法的演算法則；另外在切換律的運用上，我們探討切換時機的一些特性與相關模擬討論。

This thesis addresses the equivalence of three conditions for the existence of stabilizing switching laws between two unstable linear systems. One condition is used mainly for theoretical derivation, while the others are implementable and a class of stabilizing switching laws have been explicitly constructed by [14]. With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems it then proposed. The controllers and stabilizing switching laws are also explicitly constructed through the use of an existed algorithm.