臺灣博碩士論文加值系統

在本論文中，吾人將考慮一類具有輸入延遲和Neutral擾動之不確定時延系統之漸近穩定性分析。Lyapunov穩定理論將應用來保證在這樣的系統架構之下能夠漸近穩定化之結果。並以(1)極點指定， (2)雷卡地方程式， (3)線性矩陣不等式等方法並輔以遺傳演算法來協助證明吾人的結果。最後將各以幾個範例來說明其主要結果。

In this dissertation, the asymptotic stability analysis for a class of uncertain time-delay systems with input delay and neutral-type perturbation is considered. Lyapunov stability theory is applied to guarantee the asymptotic stability for such systems. We will use (1) pole assignment, (2) Riccati equation, (3) linear matrix inequality (LMI), to guarantee our result. The genetic algorithm (GA) is also used to solve this problem. Finally, some numerical examples are given to illustrate our obtained results.

CONTENTS
頁次
誌謝 i
摘要 ii
ABSTRACT iii
NOMENCLATURE iv
CHAPTER 1 INTRDUCTION 1
1.1 Motivation and Introduction 1
1.2 Genetic Algorithm 3
1.3 Brief Sketch of Contents 7
CHAPTER..2 MATHEMATICAL FUNDAMENTAL
AND PROBLEM FORMULATIONS 9
2.1 Some Definitions and Lemmas 9
2.2 Problem Formulation 12
2.3 Assumptions 13
CHAPTER..3 ROBUSTNESS FOR POLE ASSIGNMENT
CONTROL OF TIME-DELAY SYSTEM 15
3.1. Introduction 15
3.2. Main Results 15
3.3 Illustrative Examples 21
CHAPTER..4 ROBUSTNESS FOR TIME-DELAY SYSTEM WITH
THE OPTIMAL CONTROL OF DELAY-FREE SYSTEM 27
4.1 Introduction 27
4.2 Main Result 28
4.3 Illustrative Example 33
CHAPTER..5 ROBUST CONTROL FOR TIME-DELAY SYSTEM
— VIA LMI APPROACH 41
5.1. Introduction 41
5.2….Main Result 42
5.3. Illustrative Example 48
CHAPTER..6 CONCLUSION AND FUTURE RESEARCH 52
6.1 Conclusion 52
6.2 Future Research 52
REFERENCES

REFERENCES
[And.1] Anderson, B. D. O. and Moore, J. B., Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, 1990.
[Apk.1] Apkarian, P., Hoang D. T., and Bernussou, J., “Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations,” IEEE Transactions on Automatic Control, Vol. 46, pp. 1941 —1946, 2001.
[Boy.1] Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
[Cal.1] Callier, F. and Desoer, C., Linear System Theory, Springer-Verlag, New York, 1991.
[Cha.1] Chang, W. D., Lin, Y. L., and Chen, H. C., “A real-coded genetic algorithm for parameters estimation of nonlinear systems,” 2002 Conference on Industrial Automatic Control & Power Application, pp. C2-6 — C2-12.
[Cha.2] Chang , Y. H. and Wise, G. L., “Robust pole assignment via dependently structured perturbations using real stability radii,” Proceedings of the 34th IEEE Conference on Decision and Control, Vol. 4, pp. 3690 —3695,
1995
[Cho.1] 周鵬程， 遺傳演算法原理與應用 活用Matlab，全華科技圖書股份有限公司，台北，1991.
[Dug.1] Dugard, L. and Verriest, E. I., Stability and Control of Time-delay Systems, Springer-Verlag, London, 1997.
[Fan.1] Fan, K. G., Some Aspects of Neutral Systems: Stability Analysis and Stabilization. Ph.D. Dissertation, Sun Yat-Sen University, Kaohsiung, 2002.
[Hal.1] Hale, J. K. and Verduyn Lunel, S. M., Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
[Hor.1] Horm, R. A. and Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, 1985.
[Hu.1] Hu, G. D. and Hu, G. D., “Stabilization of an uncertain large-scale time-dependent bilinear neutral differential system by memory feedback control,” IMA Journal of Control and Information, Vol. 18, pp. 1-18, 2001.
[Jua.1] Juang, Y. T., Kuo, T. S. and Hsu, C. F., “Stability robustness analysis of digital control systems in state-space models,” International Journal of Control. Vol. 46, pp. 1547-1556, 1987.
[Kol.1] Kolmanovskii, V. B. and Myshkis A., Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publ., Dordrecht, 1999.
[Kol.2] Kolmanovskii, V. B. and Richard, J. P., “Stability of some linear systems with delays,” IEEE Transactions Automatic Control, Vol. 44, pp. 984-989, 1999.
[Kua.1] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
[Lie.1] Lien, C. H. and Hsieh, J. G., “New results on global exponential stability of interval time-delay systems,” JSME International Journal, Series C, Vol. 43, pp. 306-310, 2000.
[Lie.2] Lien, C. H. and Chen, J. D., “Discrete-delay-independent and discrete -delay-dependent criteria for a class of neutral systems,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 125, pp. 33-41, 2003.
[Lie.3] Lien, C. H. Hsieh, J. G. and Sun, Y. J., “Robust stabilization for a class of uncertain systems with multiple time delays via linear control,” Journal of Mathematical Analysis and Applications, Vol. 218, pp. 369-378, 1998.
[Lie.4] Lien, C. H. Sun, Y. J., and Hsieh, J. G., “Global stabilizability for a class of uncertain systems with multiple time-varying delays via linear control,” International Journal of Control, Vol. 72, pp. 904-910, 1999.
[Lie.5] Lien, C. H., Some Aspects of Uncertain Time-delay Systems: Stability Analysis and Stabilization, Ph.D. Dissertation, Sun Yat-Sen University, Kaohsiung, 1998.
[Liu.1] 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.
[Luo.1] Luo, R. C. Chung, L. Y., and Lien, C. H., “Stabilization for linear uncertain system with time latency,” IEEE Transactions on Industrial Electronics, Vol. 49, pp. 905-910, 2002.
[Ort.1] Ortega, J. M., Numerical Analysis, Academic Press, New York, 1972.
[Ran.1] Randy, L. H. and Sue, E. H., Practical Genetic Algorithms, John Wiley & Sons, New York , 1998.
[Su.1] Su, T. J. and Liu, P. L., “Robust stability for linear uncertain time-delay systems with delay-dependence,” International Journal of Systems Science, Vol. 24, pp. 1067-1080, 1993.
[Sun.1] Sun, Y. J., Lee, C. T. and Hsieh, J. G., “Sufficient conditions for the stability of interval systems with multiple time-varying delays,” Journal of Mathematical Analysis and Applications, Vol. 207, pp. 29-44, 1997.
[Tis.1] Tissir, E. and Hmamed, A., “Stability tests of interval time delay systems,” Systems & Control Letters, Vol. 23, pp. 263-270, 1994.