指導教授：馮蟻剛臺灣大學：電機工程學研究所林群弼Lin, Chun-PiChun-PiLin2014-11-282018-07-062014-11-282018-07-062014http://ntur.lib.ntu.edu.tw//handle/246246/262918本論文中研究三個主題，第一：針對具有多個時滯狀態的線性多時延系統進行穩定性分析，假設這些系統中時滯長度會在固定區間內變化，時延相關的指數穩定性分析條件是以線性矩陣不等式的型式呈現。為了降低條件的保守性，本論文使用新的李亞普諾夫函數，包含了更完整的狀態資訊，使得在定理推導過中可以將時變時滯視為不確定參數。第二：當考慮到時變時滯長度的變化下限大於或等於零時，建立一時延參數相關的李亞普諾夫函數，以分析具有一個非遞減時滯長度之時延系統。本論文所提出之理論藉由數值範例以及直流馬達模型之應用進行說明，以驗證其應用方式及效能。第三：針對連續時間系統提出一種數位準比例微分控制器，以達系統之指數穩定化。本論文所提出的控制方法則可視為傳統PDP控制之一種變形，不同點在於本論文提出的控制法則僅使用系統輸出的取樣訊號，因此較易於實現且實用。此部分所提出的控制器藉由應用於二階負阻尼系統及一雙倒單擺系統來驗證其效能及可行性。This dissertation studies a general class of linear systems with multiple successive delay components. First of all, the delays are assumed to vary in intervals, and delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities. To reduce conservativeness, a new Lyapunov-Krasovskii functional is designed to contain more complete state information, so that a derivation procedure with time-varying delays treated as uncertain parameters can be adopted. Secondly, when the lower bound of time-varying delay’s rate of change is greater than or equal to zero, a delay-parameter-dependent Lyapunov functional is built to analyze the stability of linear systems with a non-decreasing time-varying delay. Pure numerical examples as well as an example with a DC motor model are provided to demonstrate the effectiveness of the proposed stability criteria. Finally, a digital quasi-PD controller is proposed to achieve exponential stabilization for linear continuous-time systems. As a variation of the traditional position and delayed position (PDP) control, the proposed controller uses samples of the output signals, which is easier to implement and more practical. A second-order negatively damped system and a double inverted pendulum system are tested to show the control method is effective.誌謝 I 摘要 II Abstract III Content IV List of Figures V List of Tables V Chapter 1 Introduction 1 1.1 Background 1 1.2 Organization 6 1.3 Notations 7 Chapter 2 Exponential stability analysis of linear systems with multiple successive delay components 8 2.1 Problem formulation 8 2.2 Exponential stability analysis 9 2.3 Two special cases and numerical examples 21 Chapter 3 Parameter-dependent Lyapunov functional for linear systems with a time-varying delay 29 3.1 Problem formulation 29 3.2 Stability analysis for both nominal and uncertain system 30 3.3 Numerical examples 38 Chapter 4 Stability analysis of sampled-data control systems 41 4.1 Problem formulation 41 4.2 A DC motor example 42 4.2.1. Considering non-uniform sampling 45 4.2.2. PID type controller with non-uniform sampling and delay rate 48 Chapter 5 Exponential stabilization of linear systems using discrete-time quasi-PD controller 53 5.1 Problem formulation 53 5.2 Synthesis conditions 57 5.3 Numerical examples 63 Chapter 6 Conclusions and future works 68 6.1 Conclusions 68 6.2 Future works 68 References 704112132 bytesapplication/pdf論文公開時間：2015/09/03論文使用權限：同意有償授權(權利金給回饋學校)時延系統時變時滯多時滯系統穩定性線性矩陣不等式比例微分控制器thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/262918/1/ntu-103-D94921008-1.pdf