# 臺灣博碩士論文加值系統

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 本篇論文針對一類不確定離散系統，提出一套保證其不穩定之判別準則，此判別準則，僅需計算兩個特定多項式函數之非負解，最後我們提供一個數值範例來說明我們的主要定理。
 In this thesis, simple criteria for the instability of a class of uncertain discrete systems are derived. Such criteria can be easily checked by estimating the largest nonnegative zero of two specific polynomials. A numerical example is also provided to illustrate the main results.
 目錄中文摘要...............................................................i英文摘要..............................................................ii目錄.................................................................iii圖目錄................................................................iv第一章 前言............................................................11.1 研究背景與動機.....................................................11.2 符號定義...........................................................3第二章 定義與定理......................................................52.1 離散時間系統與轉換.................................................52.2 多項式(polynomial)................................................222.3 穩定性的定義......................................................262.4 環形界限..........................................................31第三章 主要定理3.1 系統描述..........................................................333.2 主要定理..........................................................38第四章 結論與未來研究方向.............................................434.1 結論..............................................................434.2 未來研究方向......................................................43參考文獻..............................................................45
 參考文獻[1] Boese, F. G. and Luther, W. J., 1989, A Note on a Classical Bound for the Moduliof All Zeros of Polynomial, IEEE Trans. Automat. Contr., Vol. 76, pp. 998-1001.[2] Benjamin, C.K., 1992, Digital Control System, Harcount Brace Jovanovich ,Florida.[3] Bronshtein I.N. and Semendyayev, K. A.1979, Handbook of Mathematics, VenNostrand Reinhold Company Inc, New York.[4] Chu, D., Lathauwer, L.D., Moor, B.D., 2001, On the computation of the restrictedsingular value decomposition via the cosine-sine decomposition, SIAM Journal onMatrix Analysis and Applications , Vol.22 , pp.580-601.[5] Datt, B. and Govil, N. K., 1978, On the Location of Zeros of Polynomial, J.Approx.Theory, Vol. 24, pp. 78-82.[6] Han H. S. and Lee J. G. Lee, 1993, Stability Analysis of Interval Matrices byLyapunov Function Approach Including ARE, Control--Theory and AdvancedTechnology, Vol. 9, pp. 745-757.[7] Joyal, A., Labelle, G. and Rahman, Q. I., 1967, On the Locations of Zeros ofPolynomials, Canadian Math. Bulletin, Vol. 10, pp. 53-63.[8] Ledermann, W. and Vajda, S., 1980, Handbook of Applicable Mathematics,Canadian Mathematical Bulletin, John-Wiley & Sons, New York, USA.[9] Ogata, K., 1987, Discrete-time Control System , Englewood Cliffs, Prentice Hall,NJ.[10] Phillips, C.L. and Nagle,H.T., 1991, Digital Control System Analysis and Design,Prentice Hall Inc, NJ.[11] Salivahanan, S., Vallavarai, A. and Gnanapriya, C., 1999, Digital SignalProcessing,McGraw Hill Companies, Inc.[12] Sun, Y. J., 2003a, Simple Instability Criteria for a Family ofComplex-Coefficient Polynomials, Journal of the Chinese Institute of ElectricalEngineering, Vol. 26, No. 3, pp. 371-374.[13] Sun, Y. J., Horng, J. H. and Hsieh, J. G., 1996a, A Note on the Circular Bound ofPolynomial Zeros, IEEE Trans. Circuits Syst., Vol. 43, pp. 476-478.[14] Sun, Y. J., Horng, J. H. and Hsieh, J. G., 1996b, Annular Bounds for the Zeros of aFamily of Complex-Coefficient Polynomials, Journal of the Chinese Institute ofElectrical Engineering, Vol. 3, pp. 97-100.[15] Sun, Y. J., 2003b, Annular Bounds for the Roots of Characteristic Equations ofUncertain Discrete Systems, ASME Journal of Dynamic Systems, Measurement,and Control, Vol. 125, No. 2, pp. 202-204.[16] Sun, Y. J., 2004, New Result for the Annular Bounds of Complex-CoefficientPolynomial Zeros, IEEE Transactions on Automatic Control, Vol. 49, No. 5, pp.813-814.[17] Zeheb, E., 1991, On the Largest Modulus of Polynomial Zero, IEEE Trans.Circuits Syst., Vol. 38, pp. 333-337.[18] Zilovic, M. S., Roytman, L. M., Combettes, P. L. and Swamy, M. N. S., 1992, ABound for the Zeros of Polynomials, IEEE Trans. Circuits Syst., Vol. 39, pp.476-478.[19] B. C. Kuo , 1987, Automatic Control System , 5th ed,. 歐亞。[20] 林超群，1999, 自動控制系統設計與Matlab 語言，全華。[21] 周建華，2000, 矩陣原理及題解，中央圖書。
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 1 一類不確定離散系統之保證A[r,R)不穩定判別準則

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