臺灣博碩士論文加值系統

本論文討論擁有不穩定子系統的線性開關系統，以及連續廣義開關系統的可穩定化開關訊號之設計，其中針對線性開關系統，本文以”李代數”分析其解之形式，進而找到可穩定化此系統的開關訊號，而針對連續廣義開關系統，本文以和一般傳統Lyapunov functional較不相同的”不連續Lyapunov functional”，來尋找可穩定化此系統的開關訊號。

This thesis focuses on the design of switch signal, it can stabilize switched linear system which contains an unstable subsystem, and switched singular systems. Especially, as for switched linear system, this thesis employs Lie Algebra analysis to locate switch signal to stabilize the system. Furthermore, for switched singular system, unlike traditional Lyapunov functional method, this thesis employs discontinuous Lyapunov functional method to locate the switch signal which can stabilize the system.

摘要 i
第一章 緒論 1
1-1 節 文獻回顧與研究動機 1
1-2 節 論文綱要 2
第二章 李代數之性質與數學基礎 3
第三章 有不穩定子系統的線性開關系統穩定度之分析及設計 8
3-1 節 具有兩個子系統的線性開關系統之穩定化控制 8
3-2 節 具有三個子系統的線性開關系統之穩定化控制 10
3-3 節 數據模擬 16
第四章 廣義開關系統之穩定度分析及設計 18
4-1 節 系統基本性質 18
4-2 節 子系統數為三的廣義開關系統之穩定度分析及設計 20
4-3 節 數據模擬 26
第五章 結論 29
參考文獻 30

圖 次
3.1 例3-1系統狀態分解圖 16
3.2 例3-1系統狀態分解圖 16
3.3 例3-1系統狀態分解圖 16
3.4 例3-2系統狀態分解圖 17
3.5 例3-2系統狀態分解圖 17
3.6 例3-2系統狀態分解圖 17
4.1 例4-1系統狀態圖 27
4.2 例4-1系統狀態分解圖 27
4.3 例4-1系統狀態分解圖 28
4.4 例4-1系統狀態分解圖 28

[1]D. Liberzon, J. P. Hespanha, A. S. Morse, “Stability of switched systems: a Lie-algebraic condition,” Systems &; Control Letter, vol. 37 pp. 117-122, 1998.
[2]L. Gurvits, “Stability of discrete linear inclusion,” Lin. Algebra Appl., 231 pp.47-85, 1995.
[3]G. Zhai, X. Xu, H. Lin, and A. N. Michel, “Analysis and design of switched normal systems,” Nonlinear Analysis: Theory, Methods &; Applications, vol. 65, no. 12, pp. 2248-2259, 2006.
[4]J. P. Hespanha, A. S. Morse, “Stability of switched systems with average dwell –time,” Conference on decision &; control, pp. 2655-2660, 1999.
[5]H. Ishii, B. A. Francis, “Stabilizing a linear system by switching control with dwell time,” American Control Conference, pp. 1876-1881, 2001.
[6]W. A. Zhang and L. Yu, “Stability analysis for discrete-time switched time-delay systems,” Automatica, vol. 45, no 10, pp. 2265-2271, 2009.
[7]J. Lin, Z. Gao, “Exponential admissibility and control of switched singular time-delay systems: an average dewell time approach,” Journal of applied mathematics, pp. 1-28, 2012.
[8]J. C. Geromel and P. Colaneri, “Stability and stabilization of continuous-time switched linear systems,” SIAM J. Control Optim., vol. 45, no. 5, pp. 1915-1930, 2006.
[9]X. M. Sun, G. P. Liu, and and J. Zhao, “Stability Analysis for Linear Switched Systems With Time-Varying Delay,”IEEE Trans. Syst., Man. Cybern. B, Cybern., vol. 38, no. 2, pp.528-533, 2008.
[10]H. Samelson, “Notes on Lie Algebra,” Springer-Verlag.
[11]D. Liberzon, “Switching in Systems and Control,” Boston, MA:Birkhauser, pp.31 2003.
[12]S. Xu, J. Lam, “Robust Control and Filter of Singular Systems,” Berlin, Germany: Springer-Verlag.