臺灣博碩士論文加值系統

摘要
本篇論文主要是從微分局論的觀點針對線性非時變描述子系統來探討H∞控制問題，在推導H∞控制所對應之廣義Riccati不等式過程中
，吾人可以發現系統的外來輸入w及控制輸入u彼此間互相競爭消長
的情形，同時所推導出相對應之廣義Riccati不等式正可和廣義界實引理所得到的廣義Riccati方程式作一對照。
關鍵字: H∞控制 ，描述子系統，微分局論。

Abstract
Based on a differential game approach, this thesis is mainly concerned with the H∞ control problem for linear time-invariant descriptor systems with D11 ≠ 0. In the derivation of the associated generalized algebraic Riccati inequalities (GARIs) with the H∞ problem, a deeper insight is provided into the essential feature of energy competition between the exogenous input w and the control input u. With D11 = 0, comparison of the results obtained here with the results obtained by Wang et al. (1998) is also given.
Keywords: H∞Control，Descriptor Systems，Differential Game。

本文目錄
第一章 簡介 3
第二章 數學基礎與背景知 5
2.1 描述子系統之數學描述………………………………5
2.2 描述子系統之穩定度,可控性,可觀性………………6
2.3 描述子系統之Lyapunov穩定度定理…………………7
2.4 描述子系統H∞ 問題敘述……………………………8
2.5廣義界實引理(Generalized Bounded Real Lemma) 9
2.6微分局論簡介…………………………………………10
第三章 H∞狀態回授控制 12
3.1 前言……………………………………………………12
3.2 廣義Riccati不等式解…………………………………12
第四章 H∞輸出回授控制 18
4.1 前言……………………………………………………18
4.2 利用分離原理設計輸出回授控制器…………………19
4.3 廣義Riccati不等式解………………………………21
第五章 結論 29

[1] J. Bender and A. J. Laub, "The Lineal-Quadratic Optimal
Regulator for Descriptor Systems," IEEE Transactions on
Automatic Control,Vol. AC-23,No1,672-688,1987.
[2] F. R. Gantmacher, The Theory of Matrices, Vol I and II,
Chelsea,New Yorl,1959.
[3] H. W. Knobloch,A. Isidori,and D. Flockerzi,Topics in
Control Theory,Birkhauser,1993.
[4] H. S. Wang, C. F.Yung,and F. R. Chang,"Bounded Real Lemma
and H∞ Control for Descriptor Systems," IEE Proceeding D:
Control Theory and Its Applications, Vol.145,No3,pp.316-322,
1998.
[5] H. S. Wang,H∞ Control for Nonlinear Descriptor Systems, Ph.
D. Dissertation, Dept. of Electrical Engineering, National
Taiwan Unversity,1999.
[6] G. Zames,"Feedback and optiaml sensitivity:modelreference
transformations,multiplicative seminorms,and approximate
inverses,"IEEE Trans. Automat Control.,Vol 26,pp.301-
320,1981.
[7] 容志輝,"正實控制理論",未發表之上課講義,1997.