臺灣博碩士論文加值系統

在本論文中，將考慮經由切換訊號設計來探討具時變時間延遲和分式擾動之不確定離散切換系統H∞性能分析和H∞切換控制之研究。將提出簡易切換訊號設計法則以使考慮之切換系統能保證系統性能要求，並提出新的李雅普諾夫泛函數和更彈性切換訊號設計方法藉由LMI準則以保證離散切換時間延遲系統之H∞性能分析和H∞ 切換控制。新型延遲分割法及Jensen不等式被用來改善所的結果的保守性。本文可以較少的LMI變數，得到比已發表文獻更佳之結果。最後，將以一些數值例子來說明所得成果的重大改進。

In this thesis, the H∞ performance analysis and switching control of uncertain discrete switched systems with interval time-varying delay and linear fractional perturbations are considered via switching signal design. New Lyapunov functional and more flexible switching signal design are proposed to derive some LMI conditions which guarantee the H∞ performance of discrete switched time-delay system.
Novel delay-partitioning approach and Jensen inequality are used to improve the conservativeness of proposed results. The used number of LMI variables is less than some published results. Finally, some numerical examples are illustrated to show the major improvement of the proposed results.

摘要 I
ABSTRACT II
致謝 III
CONTENTS IV
LIST OF TABLE VI
LIST OF FIGURES VII
NOMENCLATURE VIII
CHAPTER 1 INTRODUCTION 1
1.1 Background and Motivation 1
1.2 Brief Sketch of the Contents 4
CHAPTER 2 MATHEMATICAL PRELIMINARIES 5
CHAPTER 3 NOVEL DELAY-PARTITIONING APPROACH ON STABILITY OF UNCERTAIN DISCRETE SWITCHED TIME-DELAY SYSTEMS VIA SWITCHING SIGNAL DESIGN 9
3.1 Problem Statement 9
3.2 Illustrative Examples 20
CHAPTER 4 ROBUST PERFORMANCE AND SWITCHING CONTROL FOR UNCERTAIN DISCRETE SWITCHED SYSTEMS WIYH INTERVAL TIME-VARYING DELAY 25
4.1 Problem Formulation and Preliminaries 25
4.2 Robust Switching Control for Switched System 34
4.3 Illustrative Examples 42
CHAPTER 5 CONCLUSIONS 51
REFERENCES 52

 

[BOYD.1] BOYD, S. P., GHAOUI, L. El, FERON, E., & BALAKRISHNAN, V. (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM.
[CHAN.1]CHANG, X. H. (2012) Robust nonfragile filtering of fuzzy systems with linear fractional parametric uncertainties. IEEE Trans. Fuzzy Systems, 20, 1001–1011.
[GU.1] GU, K., KHARITONOV & V. L., & CHEN, J. (2003) Stability of Time-Delay Systems. Boston, Massachusetts: Birkhauser.
[HALE.1]HALE, J. K. & VERDUYN LUNEL, S. M. (1993) Introduction to Functional Differential Equations. New York: Springer-Verlag.
[IBR.1] IBRIR, S., (2008) Static output feedback and guaranteed cost control of a class of discrete-time nonlinear systems with partial state measurements. Nonlinear Analysis, 68, 1784–1792.
[KOKI.1] KOKIL, P., KANDANVLI, V. K. R., & KAR, H. (2013) Delay-partitioning approach to stability analysis of linear discrete-time systems with interval-like time-varying delay. Int. J. Engineer. Math., 291976, 1-7.
[KOLM.1]KOLMANOVSKII, V. B. & MYSHKIS A. (1992) Applied Theory of Functional Differential Equations. Netherlands: Kluwer Academic Publishers.
[LI.1] LI, T., GUO, L., & SUN, C. (2007) Robust stability for neural networks with time-varying delays and linear fractional uncertainties. Neurocomputing, 71, 421-427.
[LI.2] LI, Z., GAO, H., & KARIMI, H. R. (2014) Stability analysis and controller synthesis of discrete-time switched systems with time delay. Systems Control Lett., 66, 85-93.
[LIEN.1] LIEN, C. H., YU, K. W., CHUNG, Y. J., CHANG, H. C., CHUNG, L. Y., & CHEN J. D. (2011) Exponential stability and robust control for uncertain discrete switched systems with interval time-varying delay. IMA J. Math. Control Inform., 28, 121-141.
[LIEN.2] LIEN, C. H., YU, K. W., CHUNG, Y. J., CHANG, H. C., CHUNG, L. Y., & CHEN J. D. (2011) Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay. Nonlinear Analysis: Hybrid Systems, 5, 10-19.
[LIEN.3] LIEN, C. H., YU, K. W., CHEN, J. D. & CHUNG, L. Y. (2013) Sufficient conditions for global exponential stability of discrete switched time-delay systems with linear fractional perturbations via switching signal design. Advances in Difference Equations, 2013: 39, 1-15.
[LIEN.4]LIEN, C. H, YU, K. W, Chung, L. Y., & Chen, J. D. (2013) performance for uncertain discrete switched systems with interval time-varying delay via switching signal design. Applied Mathematical Modelling, 37, 2484-2494.
[LIEN.5]LIEN, C. H, YU, K. W, Wu, L. C., Chen, J. D., Chung, L.Y. (2014) Robust switching control and switching signal design for uncertain discrete switched systems with interval time-varying delay. Journal of the Franklin Institute, 351, 565-578.
[MAHM.1]MAHMMOUD, M. S. (2010) Switched Time-Delay Systems. Boston, Springer-Verlag.
[MAHM.2]MAHMMOUD, M. S., NOUNOU, H. N., & XIA, Y. (2010) Robust dissipative control for internet-based switched systems. Journal of the Franklin Institute, 347, 154-172.
[MENG.1] MENG, X., LAM, J., DU, B., & GAO, H. (2010) A delay-partitioning approach to the stability analysis of discrete-time systems. Automatica, 46, 610-614.
[PHAT.1] PHAT, V. N. BOTMART, T., & NIAMSUP, P. (2009) Switching design for exponential stability of a class of nonlinear hybrid time-delay systems. Nonlinear Analysis: Hybrid Systems, 3, 1-10.
[PHAT.2]PHAT, V. N. & RATCHAGIT, K. (2011) Stability and stabilization of switched linear discrete-time systems with interval time-varying delay. Nonlinear Analysis: Hybrid Systems, 5, 605-612.
[QIAN.1] QIAN, W. (2010) Improved stability analysis on delayed neural networks with linear fractional uncertainties. Appl. Math. Comput., 217, 3596-3606.
[SANG.1] SANGAPATE, P. (2012) New sufficient conditions for the asymptotic stability of discrete time-delay systems. Advances in Difference Equations, 2012: 28, 1-8.
[SUN.1] SUN, Y. G., WANG, L., & XIE G. (2007) Delay-dependent robust stability and control for uncertain discrete-time switched systems with mode-dependent time delays. Appl. Math. Comput., 187, 1228-1237.
[SUN.2] SUN, Z. & GE, S. S. (2005) Switched Linear Systems Control and Design. London: Springer-Verlag.
[XIAN.1] XIANG, W. & XIA, J. (2011) finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. Journal of the Franklin Institute, 348, 331-352.

[YANG.1] YANG, J., LUO, W., LI, G., & ZHONG, S. (2010) Reliable guaranteed cost control for uncertain fuzzy neutral systems. Nonlinear Analysis: Hybrid Systems, 4, 644-658.
[ZHAN.1] ZHANG, L., SHI, P., & BASIN, M. (2008) Robust stability and stabilisation of uncertain switched linear discrete time-delay systems. IET Control Theory & Applications, 2, 606-614.
[ZHAN.2] ZHANG, W. A. & YU, L. (2008) New approach to stabilisation of networked control systems with time-varying delays. IET Control Theory & Applications, 2, 1094-1104.
[ZHAN.3] ZHANG, W. A. & YU, L. (2009) A robust control approach to stabilization of networked control systems with time-varying delays. Automatica, 45, 2440-2445.
[ZHAN.4] ZHANG, W. A. & YU, L. (2009) Stability analysis for discrete-time switched time-delay systems. Automatica, 45, 2265-2271.
[ZHU.1] ZHU, X. L. & YANG, G. H. (2008) Jensen inequality approach to stability analysis of discrete time systems with time-varying delay. Proc. Amer. Control Conf., 1644–1649.