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研究生:林詠盛
研究生(外文):Yong-Sheng Lin
論文名稱:區間時變時滯線性系統穩定條件的新分析結果
論文名稱(外文):New Delay-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay
指導教授:練光祐
口試委員:曾傳蘆王偉彥馮蟻剛張帆人
口試日期:2012-07-23
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:電機工程系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:64
中文關鍵詞:時變時滯穩定性時滯系統線性矩陣不等式
外文關鍵詞:Time-varying DelayStabilityTime-delay systemsLinear matrix inequality (LMI)
相關次數:
  • 被引用被引用:1
  • 點閱點閱:103
  • 評分評分:
  • 下載下載:4
  • 收藏至我的研究室書目清單書目收藏:0
本論文以Lyapunov-Krasovskii方法針對區間時變時滯線性系統,推導與區間延遲相關的穩定性。推導過程中適時使用自由權重法、Jensen積分不等式及凸集合技術來儘可能放寬穩定條件,並以線性矩陣不等式的形式表示最終的結果。由數值範例的比較,明確地呈現出本論文所提出的方法確實能夠達到文獻上迄今最好的結果。為取得創新的結果,首先我們提出一個新穎的增廣Lyapunov泛涵,其特色是將區間時變時滯線性系統下界的時滯區間分成多個等距的子區間,接著在每個子區間及時滯區間構築含有三重積分在內的增廣Lyapunov泛涵。接著,利用自由權重法及Jensen積分不等式來處理該增廣Lyapunov泛涵對時間取導數後產生的積分項。然後為了避免以往因過度界定時變時滯項而造成不可避免的保守性發生,我們引入凸集合技術來完成最終的推導,於是區間時變時滯線性系統的穩定條件可以線性矩陣不等式的型式表示之。最後,由數值範例來證實本論文所提出的方法確實比以往的結果顯著的改善了保守性。

In this thesis, the delay-range-dependent stability of linear systems with interval time-varying delay will be studied. It is mainly based on Lyapunov-Krasovskii methodology. The derivation techniques include the delay free weighting matrix (FWM) method, Jensen''s integral inequality, the convex combination technique, and the linear matrix inequality (LMI). Stability criteria are given in terms of LMIs, and numerical examples are given to illustrate the effectiveness and the merits of the results. To this end, we first decompose the lower bound delay interval into multiple equidistant subintervals, then construct augmented Lyapunov functionals which contains some triple-integral terms on these intervals and the time-varying delay interval. Consequently, a novel augmented Lyapunov functional is proposed. Secondly, by using FWM approach, Jensen''s integral inequality and the convex combination technique, some new stability criteria for interval time-varying delay systems are derived in terms of LMIs. Finally, numerical examples are presented to demonstrate the less conservatism of the obtained results, when compared to existing results.

摘 要 i
ABSTRACT ii
致 謝 iii
Contents iv
List of Tables vi
List of Figures vii
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 3
1.3 Review of Delay-Dependent Stability Analysis for Interval Time-Delay Systems 4
1.4 Purpose and Contribution 6
1.5 Organization of the Thesis 7
Chapter 2 Preliminary 9
2.1 Stability of Time-Delay Systems 9
2.1.1 Time-Delayed Mathematical Models 9
2.1.2 Stability Concept 10
2.1.3 Lyapunov-Krasovskii Stability Theorem 11
2.2Linear Matrix Inequality (LMI) Method 12
2.2.1 General Form of LMIs 13
2.2.2 A Simple Example of LMI Method 13
2.3 Facts and Lemmas 14
Chapter 3 Main Skills for Deriving Stability Conditions 17
3.1 Free-Weighting-Matrix (FWM) Approach 17
3.2 Jenson Integral Inequality Approach 21
3.3 Delay Decomposition Approach 22
3.4 A Revisit to The Stability Conditions of Systems with Interval Time-Varying Delay 25
Chapter 4 New Stability Criteria of Interval Time-Varying Delay Systems 30
4.1 Problem Formulation 30
4.2 Construction of Lyapunov Functional 31
4.3 Main Results for Stability Conditions 33
Chapter 5 Illustrative Examples 53
Chapter 6 Conclusions and Future Work 56
References 58
Notations 63



[1] M. Zavarei and M. Jamshidi, Time-Delay Systems: Analysis, Optimization and Applications, Amsterdam: North-Holland, 1987.
[2] T. Mori, “Criteria for Asymptotic Stability of Linear Time-Delay Systems,” IEEE Trans. Automat. Contr., vol. AC-30, no. 2, 1985, pp. 158-161.
[3] S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994.
[4] K. Gu, V.L. Kharitonov and J. Chen, Stability of time-delay Systems, Boston: Birkhauser, 2003.
[5] S. Xu and J. Lam, “A survey of linear matrix inequality techniques in stability analysis of delay systems,” International Journal of Systems Science, vol. 39 no. 12, 2008, pp. 1095–1113.
[6] Y. He, Q. G. Wang, C. Lin and M. Wu, “Delay-range-dependent stability for systems with time-varying delay,” Automatica, vol. 43, no. 2, 2007, pp. 371–376.
[7] D. Yue, Q. L. Han and C. Peng, “State feedback controller design of networked control systems,” IEEE Transactions on Circuits and Systems—II: Express Briefs, vol.51, no. 11, 2004, pp. 640–644.
[8] Q. L. Han and K. Gu, “Stability of linear systems with time-varying delay: A generalized discretized Lyapunov functional approach,” Asian Journal of Control, vol. 3, no. 3, 2001, pp. 170–180.
[9] X. Jiang and Q. L. Han, “On H∞ control for linear systems with interval time-varying delay,” Automatica, vol. 41, no. 12, 2005, pp. 2099–2106.
[10] Y. He, M. Wu, J. H. She and G. P. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Systems and Control Letters, vol. 51, no. 2, 2004, pp. 57–65.
[11] E. Fridman and U. Shaked, “Delay-dependent stability and H∞ control: Constant and time-varying delays,” International Journal of Control, vol. 76, no. 1, 2003, pp. 48–60.
[12] Q. L. Han, “On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty,” Automatica, vol. 40, no. 6, 2004, pp. 1087–1092.
[13] Y. He, M. Wu, J. H. She and G. P. Liu, “Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic type uncertainties,” IEEE Transactions on Automatic Control, vol. 49, no. 5, 2004, 828–832.
[14] M. Wu, Y. He, J. H. She and G. P. Liu, “Delay-dependent criteria for robust stability of time-varying delay systems,” Automatica, vol. 40, no. 8, 2004, pp. 1435–1439.
[15] Y. He, Q. G. Wang, C. Lin and M. Wu, “Delay-range-dependent stability for systems with time-varying delay,” Automatica, vol. 43, no. 2, 2007, pp. 371-376.
[16] H. Y. Shao, “Improved delay-dependent stability criteria for systems with a delay varying in a range,” Automatica, vol. 44, no. 12, 2008, pp. 3215–3218.
[17] Q. L. Han, “Absolute stability of time-delayed systems with sector bounded nonlinearity,” Automatica, vol. 41, no. 12, 2005, pp. 2171–2176.
[18] H. Y. Shao, “New delay-dependent stability criteria for systems with interval delay,” Automatica, vol. 45, no. 3, 2009, pp. 744–749.
[19] W. Qian, C. Shen, Y. X. Sun and S. M. Fei, “Novel robust stability criteria for uncertain systems with time-varying delay,” Applied Mathematics and Computation, vol. 215, no. 2, 2009, pp. 866-872.
[20] P. G. Park and J. W. Ko, “Stability and robust stability for systems with a time-varying delay,” Automatica, vol.43, no. 10, 2007, pp.1855-1858.
[21] X. F. Jiang and Q. L. Han, “Delay-dependent robust stability for uncertain linear systems with interval time-varying delay,” Automatica, vol. 42, no. 6, 2006, pp. 1059-1065.
[22] X. Jiang and Q. L. Han, “New stability criteria for linear systems with interval time-varying delay,”Automatica, vol. 44, no. 10, 2008, pp. 2680–2685.
[23] C. Peng and Y. C. Tian, “Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay,” IET Control Theory Appl., vol. 2, no. 9, 2008, pp. 752–761.
[24] E. Fridman, U. Shaked and K. Liu, “New conditions for delay derivative-dependent stability,” Automatica, vol. 45, no. 11, 2009, pp. 2723–2727.
[25] L. Orihuela, P. Millan, C. Vivas and F. R. Rubio, “Delay-dependent robust stability analysis for systems with interval delays,” American Control Conference (ACC). Baltimore: IEEE, june 2010, pp. 4993–4998.
[26] F. Gouaisbaut and D. Peaucelle, “Delay-dependent stability of time-delay systems,” Proc. of the 5th IFAC Symposium on Robust Control Design, July 2006.
[27] J. Sun, G. P. Liu, J. Chen and D. Rees, “Improved delay-rangedependent stability criteria for linear systems with time-varying delays,” Automatica, vol. 46, no. 2, 2010, pp. 466–470.
[28] Y. Ariba and F. Gouaisbaut, “Delay-dependent stability analysis of linear systems with time-varying delay,” 46th IEEE conference on decision and control, New Orleans, USA, 2007, pp. 2053-2058.
[29] J. Sun, G. P. Liu and J. Chen, “Delay-dependent stability and stabilization of neutral time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 12, 2009, 1364-1375.
[30] A. Papachristodoulou, M. Peet, and S. Lall, "Constructing Lyapunov- Krasovskii functionals for linear time-delay systems,” American Control Conference, Portland, USA, 2005, pp. 2845-2850.
[31] Y. Nesterov and A. Nemirovskii, 1994, Interior-Point Polynomial Algorithms in Convex Programming, Philadelphia: SIAM.
[32] Q. L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, vol. 41, no. 12, Dec. 2005, pp. 2171-2176,
[33] E. Fridman and U. Shaked. “Delay-dependent stability and H∞ control: constant and time-varying delays,” International Journal of Control, vol. 76, no. 1, 2003, pp. 48-60.
[34] E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems,” Systems and Control Letters, vol. 43, no. 4, 2001, pp. 309-319.
[35] P. Park, “A delay-dependent stability criterion for systems with uncertain time-invariant delays,” IEEE Transactions on Automatic Control, vol. 44, no. 4, 1999, pp. 876-877.
[36] Y. S. Moon, P. Park, W. H. Kwon and Y. S. Lee. “Delay-dependent robust stabilization of uncertain state-delayed systems,” International Journal of Control, vol. 74, no. 14, 2001, pp. 1447-1455.
[37] E. Fridman and U. Shaked. “An improved stabilization method for linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 11, 2002, pp. 1931-1937.
[38] H. Gao and C. Wang. Comments and further results on “A descriptor system approach to H∞ control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 48, no. 3, 2003, pp. 520-525.
[39] Y. S. Lee, Y. S. Moon, W. H. Kwon, and P. G. Park. “Delay-dependent robust H∞ control for uncertain systems with a state-delay,” Automatica, vol. 40, no. 4, 2004, pp. 65-72.
[40] Y. He, Q. G. Wang, L. H. Xie and C. Lin, “Further improvement of free- weighting matrices technique for systems with time-varying delay,” IEEE Transactions on Automatic Control, vol. 52, no. 1, 2007, pp. 293–299.
[41] K. Gu, “An integral inequality in the stability problem of time-delay systems,” 39th IEEE conference on decision and control, Sydney, Australia, 2000, pp. 2805–2810.
[42] Q. L. Han, “A delay decomposition approach to stability and H∞ control of linear time-delay system—part I: stability,” 7th World Congress on Intelligent Control and Automation, Chongqing, China, June 2008, pp. 289-294.
[43] E. Fridman and U. Shaked, “A descriptor system approach to H∞ control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, Feb. 2002, pp. 253-270,
[44] M. Wu, Y. He and J. H. She, “New delay-dependent stability criteria and stabilizing method for neutral systems,” IEEE Transactions on Automatic Control, vol. 49, no. 12, Dec. 2004, pp. 2266-2271.
[45] Q. L. Han, “A delay decomposition approach to stability and H∞ control of linear time-delay system – part II: H∞ control,” Proc. Seventh World Congress on Intelligent Control and Automation, Chongqing, China, June 2008, pp. 289–294.
[46] Q. L. Han, “A discrete delay decomposition approach to stability of linear retarded and neutral systems,” Automatica, vol. 45, no. 2, 2009, pp. 517–524.
[47] Q. L. Han, “Improved stability criteria and controller design for linear neutral systems,” Automatica, vol. 45, no. 8, 2009, pp. 1948–1952.
[48] X. M. Zhang and Q. L. Han, “A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 19, no. 17, 2009, pp. 1922–1930.
[49] B. R. Li and B. G. Xu. “Improved stability criteria for linear uncertain systems with interval time-varying delay” Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P. R. China, December 16-18, 2009, pp. 7169-7174.
[50] Y. K. Su, B. Chen, W. Y. Qian and J. Sun. “New Stability Condition for Linear Systems with Time-Varying Delay,” Control and Decision Conference (CCDC), 2011 Chinese, May 23-25, 2011, pp. 3010 - 3013.
[51] J. Sun, G. Liu, J. Chen, and D. Rees, “Improved stability criteria for linear systems with time-varying delay,” IET Control Theory & Applications, vol. 4, no. 4, 2010, pp. 683-689.
[52] J. Chen, J. Sun, G. Liu, and D. Rees, “New delay dependent stability criteria for neural networks with time varying interval delay,” Physics Letters A, vol. 374, 2010, pp. 4397-4405.


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