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博碩士論文 etd-0010115-214017 詳細資訊
Title page for etd-0010115-214017
論文名稱
Title
不確定離散時變延遲奇異系統之有限時間的可容許穩定性分析
Admissible Finite-Time Stability Analysis of Uncertain Discrete-Time Singular Systems with a Time-Varying Delay
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
95
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2015-01-06
繳交日期
Date of Submission
2015-01-16
關鍵字
Keywords
可容許性、有限時間穩定性、線性矩陣不等式、延遲相關、時變延遲、離散奇異系統、自由權重矩陣
admissibility, finite-time stability, time-varying delay, discrete singular system, delay-dependent, free-weighting matrices, linear matrix inequality
統計
Statistics
本論文已被瀏覽 5684 次,被下載 48
The thesis/dissertation has been browsed 5684 times, has been downloaded 48 times.
中文摘要
本論文藉由線性矩陣不等式的方法,來研究分別以狀態空間和奇異系統模型所描述的離散時變延遲系統之分析問題。首先針對狀態空間時延系統,探討其延遲相關穩定性分析問題。我們採用里亞普諾夫方法、並結合自由權重矩陣技巧,推導得一組能確保系統漸近穩定的充分條件。然而、為了降低數值計算成本,我們使用一種有別於文獻中引入自由權重矩陣的方法,推導出含較少自由變數的充分條件,並且理論證明其與其他同樣利用自由權重矩陣法所推得條件之等價關係。有鑑於此結果在數值計算的優點,我們進一步將其推廣到針對奇異時延系統的延遲相關可容許性、與有限時間可容許性等分析問題。此外當考慮到存在於真實系統的一些不確定項和非線性項時,藉助於對這些外加項所賦予有界範數的數學描述,便能和前面提出的方法結合,而擴展本研究結果所適用的系統範疇。在推導穩定條件的各章最後,都有數值範例來說明我們所提方法的數值計算優點。
Abstract
The thesis studies, via the linear matrix inequality techniques, some analysis issues of discrete-time systems, both state-space and singular ones, with a time-varying delay. The delay-dependent stability analysis of state-space systems is addressed first. A sufficient condition for asymptotic stability is derived by the Lyapunov functional approach together with the free-weighting-matrix technique. However, aiming at reducing the number of slack variables, a different way from the existing literature to introduce the free-weighting matrices is adopted in the thesis. A theoretical proof of the equivalence between our condition and others is also provided. The results are then further extended to considering the delay-dependent admissibility and admissible finite-time stability of singular systems. To explore other possible extensions, additional time-varying norm-bounded terms, used to describe either the uncertainties or the nonlinearities, are moreover assumed existing individually in dynamics of the considered singular systems. Numerical examples to illustrate the merit of our method are also provided.
目次 Table of Contents
致謝....................................................................i
摘要...................................................................ii
Abstract............................................................iv
Contents............................................................v
List of Tables...................................................vii
List of Figures.................................................viii
List of Symbols.................................................ix
Chapter 1 Introduction......................................1
1.1 Background and Motivation.......................1
1.2 Structure of the Thesis..............................4
Chapter 2 Matrix Properties.............................6
Chapter 3 Asymptotical Stability Analysis of Discrete-Time Systems with a Time-Varying Delay..................... 9
3.1 System Description...................................9
3.2 Stability Analysis.....................................10
3.3 The Relationship between Different Stability Criteria..................... 21
3.4 Numerical Examples...................................36
Chapter 4 Admissibility Analysis of Uncertain Discrete-Time Singular Systems with a Time-Varying Delay..................... 41
4.1 System Description.................................41
4.2 Admissibility Analysis of Nominal Singular Systems......................42
4.3 Admissibility Analysis of Uncertain Singular Systems....................51
4.4 Numerical Examples...............................53
Chapter 5 Admissible Finite-Time Stability Analysis of Discrete-Time Singular Systems with a Time-Varying Delay and Nonlinear Perturbation..................... 60
5.1 System Description.................................60
5.2 Admissible Finite-Time Stability Analysis.......................................62
5.3 Numerical Examples...............................74
Chapter 6 Conclusion....................................81
Bibliography....................................................82
參考文獻 References
[1] X. Shengyuan, P. Van Dooren, R. Stefan, and J. Lam, "Robust stability and stabilization for singular systems with state delay and parameter uncertainty," IEEE Transactions on Automatic Control, vol. 47, pp. 1122-1128, 2002.
[2] S. Xu, J. Lam, B. Zhang, and Y. Zou, "New insight into delay-dependent stability of time-delay systems," International Journal of Robust and Nonlinear Control, 2013.
[3] G. Lu and D. W. C. Ho, "Generalized quadratic stabilization for discrete-time singular systems with time-delay and nonlinear perturbation," Asian Journal of Control, vol. 7, pp. 211-222, 2005.
[4] S. Ma, Z. Cheng, and C. Zhang, "Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays," IET Control Theory and Applications, vol. 1, pp. 1086-1095, 2007.
[5] Z. Du, Z. Qiu, Q. L. Zhang, and L. Liu, "New delay-dependent robust stability of discrete singular systems with time-varying delay," in Proceedings of the 7th World Congress on Intelligent Control and Automation, Chongqing, China, 2008, pp. 6359-6364.
[6] X. L. Zhu and G. H. Yang, "Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay," in Proceedings of American Control Conference, Westin Seattle Hotel, Washington, USA, 2008, pp. 1644-1649.
[7] K. F. Chen and I. K. Fong, "Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay," IET Control Theory and Applications, vol. 4, pp. 563-572, 2010.
[8] M. Fang, "Delay-dependent stability analysis for discrete singular systems with time-varying delays," Acta Automatica Sinica, vol. 36, pp. 751-755, 2010.
[9] X. Sun, Q. L. Zhang, C. Y. Yang, Y. Y. Shao, and Z. Su, "Delay-dependent stability analysis and stabilization of discrete-time singular delay systems," Acta Automatica Sinica, vol. 36, pp. 1477-1483, 2010.
[10] K. F. Chen and I. K. Fong, "Stability analysis and output-feedback stabilization of discrete-time systems with a time-varying state delay and nonlinear perturbation," Asian Journal of Control, vol. 13, pp. 1018-1027, 2011.
[11] P. Park, J. W. Ko, and C. Jeong, "Reciprocally convex approach to stability of systems with time-varying delays," Automatica, vol. 47, pp. 235-238, 2011.
[12] S. B. Stojanovic, D. L. J. Debeljkovic, and N. Dimitrijevic, "Finite-time stability of discrete-time systems with time-varying delay," Chemical Industry and Chemical Engineering Quarterly, vol. 18, pp. 525-533, 2012.
[13] K. Mathiyalagan, S. Hongye, and R. Sakthivel, "Reliable controller design for admissibility of uncertain discrete-time singular system with time-varying delay," in Proceedings of the 32nd Chinese Control Conference, Xi'an, China, 2013, pp. 1532-1537.
[14] K. Ramakrishnan and G. Ray, "Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay," Applied Mathematical Modelling, vol. 37, pp. 1468-1479, 2013.
[15] W. Xue and W. Mao, "Admissible finite-time stability and stabilization of discrete-time singular systems with time-varying delays," in Proceedings of American Control Conference, Washington, DC, USA, 2013, pp. 6072-6077.
[16] Z. Zuo, H. Li, and Y. Wang, "New criterion for finite-time stability of linear discrete-time systems with time-varying delay," Journal of the Franklin Institute, vol. 350, pp. 2745-2756, 2013.
[17] Z. Zhang, Z. Zhang, H. Zhang, B. Zheng, and H. R. Karimi, "Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay," Journal of the Franklin Institute, vol. 351, pp. 3457-3476, 2014.
[18] L. Dai, Singular Control Systems. Berlin: Springer-Verlag, 1989.
[19] S. Xu and J. Lam, Robust Control and Filtering of Singular Systems. Berlin: Springer-Verlag, 2006.
[20] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadephia, Pennsylvania: Studies in Applies Mathematics, 1994.
[21] K. Gu, K. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston USA: Birkhauser, 2003.
[22] P. Gahinet and P. Apkarian, "A linear matrix inequality approach to H-infinity control," International Journal of Robust and Nonlinear Control, vol. 46, pp. 421-448, 1994.
[23] M. Chadli and M. Darouach, "Further enhancement on robust H-infinity control design for discrete-time singular systems," IEEE Transactions on Automatic Control, vol. 59, pp. 494-499, 2014.
[24] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox : For Use with MATLAB. MA: The MathWorks, 1995.
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