臺灣博碩士論文加值系統

摘 要
本文中旨在探討近年來時延系統穩定度的強健控制系統分析，經由定理推導與例題模擬，並且求得系統可以達到漸近穩定所能容忍之最大延遲時間大小。文中引用李亞普諾夫函數Lyapunov-Krasovskii、李亞普諾夫方程式(Lyapunov equation)、與線性矩陣不等式(Linear Matrix Inequality：LMI)來研究時延系統之強健穩定分析。經由本文所得之定理求得此系統最大的時延範圍仍使系統為強健穩定，本文中以水質監控系統、熱交換控制系統與電子電路控制系統之實例討論，在控制系統能承受的最大時間延遲時間範圍內，使得系統仍能漸近穩定。

關鍵詞：李亞普諾夫函數，線性矩陣不等式，時間延遲，
延遲微分系統

Abstract
Some discussions have been made with the same examples that appear in many recent papers via illustrative examples. A neutral system with distributed time-delay is asymptotically stable. In this thesis, The control system applied the properties of the Lyapunov equation, Lyapunov -Krasovskiiand, linear matrix inequality(LMI), Newton-Leibniz formula and model transformation. These properties are employed to investigate the robust stabilization conditions. This thesis shows a maximum delay bound is derived for the robust stabilization of time-delay control systems. This thesis shows examples that the Physics mean a control system of time-delay, including Stream Water Quality, Electrical-circuit Models and Heat Exchanger Dynamics. The control system can maximum the allowable delay bound to a greater degree than the memoryless state feedback via illustrative examples. A system with distributed delay is asymptotically stable.

Keyword : Lyapunov function, Linear Matrix Inequality(LMI),
Time-delay, Neutral system.

目 錄
頁碼
中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
圖目錄 Ⅴ
表目錄 Ⅵ
第一章 緒論 1
1-1 研究動機 1
1-2 研究背景 1
1-3 文獻探討 2
1-4 章節組織 3
第二章 相關數學理論與輔助定理 5
2-1 符號說明 5
2-2 相關數學理論與輔助定理 5
第三章 水質監控控制系統 7
3-1 水質監控系統介紹 7
3-2 水質監控系統－Newton-Leibniz formula 8
3-3 水質監控系統－Model transformation 17
3-4 水質監控系統－例題模擬 25
3-5 結語 31
第四章 熱交換控制系統 32
4-1 熱交換控制系統介紹 32
4-2 熱交換控制系統－Newton-Leibniz formula 33
4-3 熱交換控制系統－Model transformation 37
4-4 熱交換控制系統－例題模擬 41
4-5 結語 46
第五章 電子電路控制系統 47
5-1 電子電路控制系統介紹 47
5-2 電子電路控制系統－Model transformation 51
5-3 電子電路控制系統－例題模擬 55
5-4 結語 58
第六章 結論與建議 59
6-1 結論 59
6-2 未來研究方向與建議 59
參考文獻 61

參考文獻
1.Boyd, S., Ghaoui, L. E., Feron, E. and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Pa:Siam, Philadelphia, 1994.
2.Castelan, W. B. and Infante, E. F., “A Lyapunov functional for matrix neutral difference equation with one delay”, Journal of Mathematics Analysis ans Application, vol. 71, pp. 105-130, 1979.
3.Chang, C. H. , Robust Stability for a Class of Uncertain Neutral Time-Delay Systems via LMI and Gas, I-Shou University, 2003.
4.Chang, C. H. , Stabilization for a class of uncertain time-delay system with input dealy and neutral-type perturbation, I-Shou University, Taiwan, 2003.
5.Chen, G. and Yang, M. and Yu, L. and Chu, J., “Delay Dependent Guaranteed Cost Control for Linear Uncertain Time-delay Systems”, Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, P. R. China, June28-July 2, 2000.
6.Desoer, C. A. and M. Vidyasagar, Feedback Systems : Input-Output Properties, Academic Press, New York, 1975.
7.Duan G. R. and Ron J. P. , “A note on Hurwitz stability of matrices”, Automatica, vol. 34, no. 4, pp. 509-511, 1998.
8.Dugard, J. and Verriest, E. I., Stability and Control of Time- delay Systems, New York : Academic Press, 1997.
9.Inamdar S. R., Kumar V. R., and Kulkarni B. D., “Dynamics of reacting systems in the presence of time delay”, Chemical Engineering Science, vol. 46, no. 3, pp. 901-908, 1991.
10.Kamen, E. W., Khargonekar P. P., and Tanenbaum A., “Stabilization of time-delay systems using finite dimensional compensators,” IEEE Transactions on Automatic Control, AC-30, pp. 75-78, 1985.
11.Kolomanovskii, V. and Myshkis A., “ Applied Theory of Functional Differential Equations”, Kluwer Academic Pub., New York, 1992.
12.Kuang, Y., Delay Differential Equation with Application in Population Dynamics, Academic Press, Boston, 1993.
13.Lam J., Gao H. and Wang C. , “ Model reduction of linear systems with distributes delay”, IEE Proc.-Control Theory Appl., vol. 152, no. 6, November 2005.
14.Li, X., Carlos E. and De Souza, “Criteria for Robust Stability and Stabilization of Uncertain Linear Systems with State Delay.Automatica”, vol. 33, no. 9, pp. 1657-1662, 1997,
15.Lien C. H., “New stability criterion for a class of uncertain nonlinear neutral time-delay systems”, International Journal of Systems Science, vol. 32, no. 2, pp. 215-219, 2001.
16.Liu, P. L., “On Delay-dependent Exponential Stability for Linear Neutral Type Time Delay Syaytem”, International Journal of Systems Science, vol. 26, no. 2, pp. 245-255, 1995.
17.Liu, P. L., “Stabilization of input delay constrained systems with delay dependence”, International Journal of Systems Science, vol. 26, no. 2, pp. 245-255, 1995.
18.Liu, P. L. and Su, T. J. , “Robust stability of interval time-Delay systems with delay-dependence”, Systems & Control Letters, vol 33, pp. 231-239, 1998.
19.Liu, P. L., “On delay dependence stabilization for uncertain neutral system with distributed delays”, Journal of Chienkuo Technology University, vol 25, no. 1, pp. 37-54, 2005.
20.Lu, C. L. and Fang, C. H., “Stability robustness bounds for uncertain circuit systems”, Journal of National Kaohsiung Institute of Technology, vol. 27, pp. 79-90, 1997.
21.Lu, C. Y. , “Robust Control of Time-Delay Systems: A Linear Matrix Inequality Approach”, National Cheng Kung University, Tainan, Taiwan, 2004.
22.Macdonald, N., Time-Lags in Biological Models, Springer-Verlag, Berlin, 1978.
23.Magdi S. M. and Naser F. Al-muthairi, “Linear parameter-varying state-delay (LPVSD) systems : stability and -gain controllers”, Systems Analysis Simulation, vol. 43, no. 7, pp. 885- 915, July 2003.
24.Magi S. M., “New results on linear parameter-varying time-delay systems “, Journal of Franklin Institute, vol. 341, pp. 675-703, 2004.
25.Mahmoud, M. S., “Robust Control and Filtering for Time-Delay Systems”, Marcel Dekker, New York, 2000.
26.Mori T. and Kokame H. , “Stability of “ , IEEE Transactions Automatic Control, vol.34. no.4. April 1989.
27.Murray, J. D., Mathematical Biology, Spring, New York , 1989.
28.Niculescu, S. I., Fu M., and Li H., “Delay-dependent closed-loop stability of linear systems with input delay: An LMI approach”, Proceedings of the 36th IEEE Conference on Decision and Control, San Fisgo, CA, 10-12, pp. 1623-1628, December, 1997.
29.Niculescu, S. I., Delay Effects on Stability, Springer-Verlag, London, 2001.
30.Phoojaruenchanachai S., Uahchinkul K. and Prempraneerach Y.,” Robust stabilisation of a state delayed system”, IEE Proc.-Control Theory Appl., vol. 145, no. 1, January 1998.
31.Roh, Y. H., and Oh J. H., “Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation”, Automatic, vol. 35, pp. 1861-1865, 1999.
32.Roh, Y. H., “Robust stability of predictor-based control systems with delayed control”, International Journal of Systems Science, vol. 33, no.2, pp. 81-86, 2002.
33.Roh, Y. H., and Oh J. H., “Robust Stability model control with uncertainty adaptation for uncertain input-delay systems”, International Journal of Control, vol. 73, no.13, pp. 1255-1260, 2000.
34.Su, T. J. and Huang, C. G.,” Robust stability of delay dependence for linear uncertain systems”, IEEE Transactions on Automatic Control, vol 37, no. 10, pp. 1656-1659, Oct. 1992
35.Trinh, H., and Aldeen M., “Stabilization of uncertain dynamic delay systems by memoryless feedback controllers”, International Journal of Control, vol. 59, pp. 1525-1542, 1994.
36.Xu S. and Lam J., ”Improved delay-dependent stability criteria for time-delay systems”, IEEE Transactions on Automatic Control, vol. 50, no. 3, March 2005.
37.Yue, D. and Han, Q. L., ”A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model”, IEEE Transactions On Circuits and Systems-II : Express Briefs , vol. 51, no. 12, December 2004.