博碩士論文 87324046 詳細資訊


姓名 吳岱儒(Day-Ru Wu)  查詢紙本館藏   畢業系所 電機工程學系
論文名稱 時延系統穩定度分析
(Analysis of Time-Delay Systems)
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摘要(中) 本論文主要針對具有時延系統的問題作進一步之研究。由於時間延遲將會改變系統的特徵方程式,因此研究方法將用來分析討論改變後的系統特徵方程式是否穩定。一般來說,當我們在檢查系統的穩定性時,若是利用延遲無關的穩定準則來測試時,可以相當簡單容易的討論,但如果利用延遲相關的穩定性準則時,通常需要比較複雜難處理的程序。由於延遲無關準則比延遲相關準則較保守,所以本論文將採用延遲相關準則來研究時延系統。
主要的研究方法將採用複變函數理論來處理由於時間延遲而改變的系統特徵方程式,然後輔以電腦軟體來分析,以發展出新的研究方法來決定時延系統的穩定性,由於以往所研究出的穩定準則所求出最大的可允許延遲區間皆從零開始,本論文的研究方法所求出的延遲區間並不一定要從零開始,而且或許有些系統可以得到一個以上的多個延遲區間使得系統在這些穩定延遲區間裡面仍具有穩定的狀態。因此應用同樣的特性來研究具有比例型時間延遲因子的時延系統,並且探討α穩定度之時延系統。
摘要(英) In this thesis, stability of linear time-invariant time-delay systems is considered. An imaginary axis intersection sequence of delay times is decided. Then some necessary and sufficient conditions for stability are derived. Therefore, the maximum delay time interval is obtained. In addition, the multiple delay time intervals allowed may be determined. And using the scheme proposed in this thesis, some examples reveal that time-delay systems stability is not necessary that the allowable delay time must vary from zero. In the sequel, stability of linear time-invariant systems with multiple time delays is considered. Finally, linear time- delay systems with decay rate that is dependent on the delay is studied. Some examples are provided to illustrate the merits of the proposed method.
關鍵字(中) ★ 比例型延遲
★ 時間延遲
★ 漸近穩定度
★ 延遲區間
關鍵字(英) ★ time delay
★ asymptotic stability
★ delay interval
★ Commensurate delays
★ decay rate
論文目次 ABSTRACT i
LIST OF FIGURES ii
CHAPTER 1 Introduction 1
1.1Motivation 1
1.2Literature Survey 2
1.3Organization of this thesis 3
CHAPTER 2 Delay Time Intervals for Stability of Time-Delay Systems 4
2.1 Introduction 4
2.2 Problem Formulation 5
2.3 Main Results 5
2.4 Examples 8
2.5 Conclusions 12
Chapter 3 Stability of Linear Time-Invariant System with Commensurate Delays 19
3.1 Introduction 19
3.2 Problem Formulation 20
3.3 Main Results 21
3.4 Examples 25
3.5 Conclusions 27
Chapter 4 Stability of Time-Delay Systems with the Decay Rate 35
4.1 Introduction 35
4.2 Problem Formulation 36
4.3 Main Results 36
4.4 Examples 41
4.5 Conclusions 45
Chapter 5 Conclusions and Future Research 51
List of Figures
Fig 2.1: The graph in (2.6) for Example 2.1 13
Fig 2.2: The plot with for Example 2.1 13
Fig 2.3: The plot with for Example 2.2 14
Fig 2.4: The graph in (2.6) for Example 2.3 14
Fig 2.5: The plot with for Example 2.3 15 Fig 2.6: The plot with for Example 2.3 15
Fig 2.7: State trajectories with time delay for Example 2.3 16
Fig 2.8: The graph in (2.6) for Example 2.4 16
Fig 2.9: The plot with for Example 2.4 17
Fig 2.10: The plot with for Example 2.4 17
Fig 2.11:State trajectories with time delay for Example 2.4 18
Fig 2.12:State trajectories with time delay for Example 2.4 18
Fig 3.1:The graph in (3.6) for Example 3.1 28
Fig 3.2: The plot with for Example 3.1 28
Fig 3.3: The plot with for Example 3.1 29
Fig 3.4: State trajectories with time delay for Example 3.1 29
Fig 3.5: State trajectories with time delay for Example 3.1 30
Fig 3.6: State trajectories with time delay for Example 3.1 30
Fig 3.7: The graph in (3.6) for Example 3.2 31
Fig 3.8: The plot with for Example 3.2 31
Fig 3.9: The plot with for Example 3.2 32
Fig 3.10:State trajectories with time delay for Example 3.2 32
Fig 3.11:State trajectories with time delay for Example 3.2 33
Fig 3.12:State trajectories with time delay for Example 3.2 33
Fig 3.13:State trajectories with time delay for Example 3.2 34
Figure 4.1: The contour D 46
Figure 4.2: The plot with and decay rate for Example 4.1 46
Figure 4.3: The plot with and decay rate for Example 4.2 47
Figure 4.4: The plot with and decay rate for Example 4.2 47
Figure 4.5: The plot with and decay rate for Example 4.3 48
Figure 4.6: The plot with and decay rate for Example 4.3 48
Figure 4.7: The plot with and decay rate for Example 4.4 49
Figure 4.8: The plot with and decay rate for Example 4.4 49
Figure 4.9: The plot with and decay rate for Example 4.5 50
Figure 4.10:The plot with and decay rate for Example 4.5 50
參考文獻 [1] J. Chiasson, “A method for computing the interval of the delay values for which a differential-delay system is stable,” IEEE Transactions on Automatic Control, Vol. 33, 1176-1178, 1988.
[2] J. Chen and H. A. Latchman, “Frequency sweeping tests for stability independent of delay,” IEEE Transactions on Automatic Control, Vol. 40, 1640-1645, 1995.
[3] J. Chen, D. Xu, and B. Shafai, “On sufficient conditions for stability independent of delay,” IEEE Transactions on Automatic Control, Vol. 40, 1675-1680, 1995.
[4] E. Cheres, S. Gutman, and Z. J. Palmor, “Stabilization of uncertain dynamic systems including state delay,” IEEE Transactions on Automatic Control, Vol. 34, 1199-1203, 1989.
[5] E. Cheres, Z. J. Palmor, and S. Gutman, “Quantitative measures of robustness for systems including delayed perturbations,” IEEE Transactions on Automatic Control, Vol. 34, 1203-1204, 1989.
[6] R. V. Churchill, J. W. Brown, and R. F. Verhey, Complex variables and Applications, McGraw-Hill Book Co., New York., 1974.
[7] L. Dugard and E. I. Verriest, “Stability and control of time-delay systems,” (p. 228) Lecture Notes in Computer Science, Berlin: Springer., 1997.
[8] J. Hale, Theory of Functional differential Equation, New York: Springer- Verlag., 1977.
[9] J. K. Hale and S. M. V. Lunel, Introduction to functional differential equations. New york: Springer., 1993.
[10] A. Hmamed, “On the stability of time-delay systems: New results,” International Journal of Control, Vol. 43, 321-324, 1986.
[11] A. Hmamed, “Further results on the delay-independent asymptotic stability of linear system,” International Journal Systems Science, Vol. 22, 1127-1132,1991.
[12] R. A. Horn and C. A. Johnson, Matrix Analysis. Cambridge University Press, New York., 1985.
[13] Y. T. Juang and W. J. Shyu, “Stability of time-delay systems,” Control-Theory and Advanced Technology, Vol. 10, 2099-2107, 1995.
[14] E. W. Kamen, “Linear systems with commensurate time delays: Stability and stabilization independent of delay,” IEEE Transactions on Automatic Control, Vol. 27, 367-375, 1982.
[15] E.W. Kamen, “Correction to ‘Linear systems with commensurate time-
delays: stability and stabilization independent of delay’,” IEEE Transactions on Automatic Control, Vol. 28, 248-249, 1983.
[16] E. B. Lee, W. S. Lu and N. E. Wu, “A Lyapunov theory for linear time-delay systems,” IEEE Transactions on Automatic Control, Vol. 31, 259-261, 1986.
[17] X. Li and C. E. de Souza, “Criteria for robust stability and stabilization of uncertain linear systems with state delay,” Automatica, Vol. 33, 1657-1662, 1997.
[18] T. Mori, “Criteria for asymptotic stability of linear time-delay systems,” IEEE Transactions on Automatic Control, Vol. 30, 158-161, 1985.
[19] T. Mori and H. Kokame, “Stability of ,” IEEE Transaction on Automatic Control, Vol. 34, 460-462, 1989.
[20] S. I. Niculescu, A. T. Neto, J. M. Dion and L. Dugard, “Delay-dependent stability of linear systems with delayed state: An LMI approach,” In Proceedings of the 34th CDC, New Orleans, LA (pp. 1495-1496), 1995.
[21] P. G. Park, “A delay-dependent stability criterion for systems with uncertain time-invariant delays,” IEEE Transactions on Automatic Control, Vol. 44, 876-877, 1999.
[22] J. H. Su, “Further results on the robust stability of linear systems with a single time delay,” Systems & Control Letters, Vol. 23, 375-379, 1994.
[23] J. H. Su, “The Asymptotic Stability of Linear Autonomous Systems with Commensurate Time Delays,” IEEE Transactions on Automatic Control, Vol. 40, 1114-1117, 1995.
[24] T. J. Su and C. G. Huang, “Robust stability of delay dependence for linear uncertain systems,” IEEE Transactions on Automatic Control, Vol. 37, 1656-1659, 1992.
[25] S. S. Wang, “Further results on stability of ,” Systems & Control Letters, Vol. 19, 165-168, 1992.
[26] K. Watanabe, M. Ito, M. Kaneko and T. Ouchi, “Finite spectrum assignment problem for systems with delay in state variables,” IEEE Transactions on Automatic Control, Vol. 28, 506-508, 1983.
[27] K. Watanabe, “Finite spectrum assignment and observer for multivariable systems with commensurate delays,” IEEE Transactions on Automatic Control, Vol. 31, 543-550, 1986.
[28] K. Watanabe, “Finite spectrum assignment of linear systems with a class of non-commensurate delays,” International Journal of Control, Vol. 47, 1277-1289, 1988.
[29] J. H. Su, “On the stability of time-delay systems,” In Proc. 33rd Conf. Decision and Control, Lake Buena, FL, pp. 429-430, 1994.
[30] J. H. Su, I. K. Fong, and C. L. Tseng, “Stability analysis of linear systems with time delay,” IEEE Transaction on Automatic Control, Vol. 39, 1341-1344, 1994.
[31] G. M. Schoen and H. P. Geering, “Stability condition for a delay differential System,” International Journal of Control, Vol. 58, 247-252, 1993.
[32] S. D. Brierley, J. N. Chiasson, E. B. Lee, and S. H. Zak, “On stabilty independent of delay for linear systems,” IEEE Transaction on Automatic Control, Vol. 27, 252-254, 1982.
[33] T. Mori, N. Fukuma, and M. Kuwahara, “ Simple stability criteria for single and composite linear systems with time delays,” International Journal of Control, vol. 34, 1175-1184, 1981.
[34] R. Datko, “A procedure for determination of the exponential stability of certain differential-difference equations,” Q. Appl. Math., 279-292, 1978.
[35] K. G. Shin and X. Cui, “Computing time delay and its effects on real-time control systems,” IEEE Transaction on Control Systems Technology, Vol. 3, 218-224, 1995.
[36] B. Lehman and K. Shujaee, “Delay independent stability conditions and decay estimates for time-varying functional differential equations,” IEEE Transaction on Automatic Control, Vol. 39, 1673-1676, 1994.
[37] T. Mori, N. Fukuma, and M. Kuwahara, “On an eatimate of the decay rate for stable linear systems,” International Journal of Control, vol. 36, pp. 95-97, 1982.
[38] C. Hou and J. Qian, “On an estimate of decay rate for applications of Razumikhin-type theorems,” IEEE Transaction on Automatic Control, Vol. 43, 958-960, 1998.
[39] M. Mahmoud and N. F. Al-Muthairi, “Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties,” IEEE Transaction on Automatic Control, Vol. 39, 2135-2139, 1994.
[40] J. Chen, G. Gu, and C. N. Nett, “A new method for computing delay margins for stability of linear delay systems,” Systems & Control Letters, Vol. 26, 107-117, 1995.
[41] J. Chen, “On computing the maximal delay intervals for stability of linear delay systems,” IEEE Transaction on Automatic Control, Vol. 40, 1087-1093, 1995.
[42] R. D. Driver, Ordinary and Delay Differential Equation, Springer-Verlag, New York, 1977.
[43] H. Gorecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, John Wiley & Sons, New York, 1989.
[44] H. Logemann and R. Rebarber, “The effects of small time-delays on the closed-loop stability of boundary control systems,” Mathematics of Control, Signals, and Systems, Vol. 9, 123-151, 1996.
[45] Y. J. Sun, J. G. Hsieh, and Y. C. Hsieh, “Exponential stability criterion for uncertain retarded systems with multiple time-varying delays,” Journal of Mathematical Analysis and Applications, Vol. 201, 430-446, 1996.
[46] Y. J. Sun, C. T. Lee, and J. G. Hsieh, “Sufficient conditions for the stability of interval systems with multiple time-varying delays,” Journal of Mathematical Analysis and Applications, Vol. 27, 29-44, 1997.
[47] H. Wu and K. Mizukami, “Exponential stabilization of a class of uncertain dynamical systems with time delay,” Control-Theory and Advanced Technology, Vol. 41, 116-121, 1996.
[48] B. Xu, “Comments on Robust stability of delay dependent for linear uncertain systems,” IEEE Transactions on Automatic Control, Vol. 39, 2365, 1994.
[49] J. S. Luo, A. Johnson, and P. J. van den Bosch, “Delay-independent robust stability of uncertain linear systems,” Systems & Control Letters, Vol. 24, 33-39,1995.
[50] G. W. Stewart, and J. G. Sun, Matrix perturbation theory, Academic Press, 1990.
[51] I. R. Petersen, and C. V. Hollot, “A Riccati equation approach to the stabilization of uncertain linear systems,” Automatic, Vol. 22, 397-411, 1986
指導教授 莊堯棠(Yau-Tarng Juang) 審核日期 2000-7-4
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