隨著通訊技術發達，訊息傳遞已成為生活中重要的課題。混沌系統於保密通訊的運用於近幾年被學者廣泛地討論及研究。本論文主要是以H∞同步來處裡切換混沌系統的應用及實現。透過李阿普諾夫穩定理論、線性矩陣不等式和線性矩陣等式，完成切換混沌系統的分析。並利用同步的特質於混沌通訊上，將欲傳遞的資料在傳送端給予混沌加密，再由接收端另一個混沌同步來達到解調的目的。本論文可分成三大部分：
(一) 混沌系統相關介紹、蔡式混沌電路以及切換系統的基本概念；
(二) 利用H∞同步處裡切換蔡式混沌系統，公式推導及模擬；
(三) 切換蔡式混沌電路之電路實現包含電路軟體模擬及硬體實現。
本論文不僅完成H∞同步於切換混沌系統並成功地將主要結果應用於一系列的保密通訊電路實現。

With the development of communication technology, message delivery has become an important issue. The applications of chaotic system have been extensively studied in recent years. This thesis demonstrates the application of switched chaotic systems with H∞ synchronization theory and circuit implementation. Based on the Lyapunov stability theory, linear matrix inequality (LMI) and linear matrix equality (LME), the synchronization of switched chaotic systems is achieved. In chaotic communication, the message is encrypted in transmitter and decrypted cipher in receiver by using the synchronization concept. This thesis is divided into three parts:
(i) The introduction of the chaotic system, Chua’s circuit and switched system concepts.
(ii) H∞ synchronization of switched Chua’s circuits, formula derived and simulation.
(iii) Implementation of the switched Chua’s circuit, including circuit simulation and hardware design.
This thesis not only achieves the H∞ synchronization in switched chaotic systems but also applies the main results to implement a class of secure communication circuit.

[1] A. El-Gohary, F. Bukhari, “Optimal control of Lorenz system during different time intervals”, Applied Mathematics and Computation, vol.144, pp.337-351, 2003.
[2] T. Botmart, P. Niamsup, “Adaptive control and synchronization of the perturbed Chua’s system”, Mathematics and Computers in Simulation, vol.75, pp.37-55, 2007.
[3] M. Rafikov, J.M. Balthazar, “On an optimal control design for Rossler system”, Physics Letters A, vol.333, pp.241-245, 2004.
[4] Y. Li, X. F. Liao, C. D. Li, Y. Wang, “On Impulsive Control for Synchronization and Its Application to Matsumoto–Chua–Kobayashi (MCK) circuit”, Communications in Theoretical Physics, vol.48, no.2, pp.275-278, 2007.
[5] Y. J. Sun, “Robust tracking control of uncertain Duffing-Holmes control systems”, Chaos, Solitons and Fractals, vol.40, pp.1282-1287, 2007.
[6] Y. Chang, G. Chen, “Complex dynamics in Chen’s system”, Chaos, Solitons and Fractals, vol.27, pp.75-86, 2006.
[7] C. Yang, Q. Zhang, L. Zhou, “Strongly absolute stability of Lur’e type differential-algebraic systems”, Journal of Mathematical Analysis and Applications, vol.336, pp.188-204, 2007.
[8] D. I. R. Almeida, J. Alvarez, J. G. Barajas, “Robust synchronization of Sprott circuits using sliding mode control”, Chaos, Solitons and Fractals, vol.30, no.1, pp.11-18, 2006.
[9] H. N. Agiza, “Chaos synchronization of Lu dynamical system”, Nonlinear Analysis, vol.58, pp.11-20, 2004.
[10] G. He, Z. Cao, P. Zhu, H. Ogura, “Controlling chaos in a chaotic neural network”, Neural Networks, vol.16, pp.1195-1200, 2003.
[11] C. Browne, “Efficient Pythagorean trees: Greed is good”, Computers & Graphics, vol.31, pp.610-616, 2007.
[12] G. T. Deng, X. G. He, Z. X. Wen, “Self-similar structure on intersections of triadic Cantor sets”, Journal of Mathematical Analysis and Applications, vol.337, no.1, pp.617-631, 2008.
[13] H. Osada, “Singular time changes of diffusions on Sierpinski carpets”, Stochastic Processes and their Applications, vol.116, no.4, pp.675-689, 2006.
[14] B. Jia, “Bounds of the Hausdorff measure of the Koch curve”, Applied Mathematics and Computation, vol.190, no.1, pp.559-565, 2007.
[15] R. C. Hilborn, “Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics”. American Journal of Physics, vol.72, pp.425–427, 2004.
[16] X. M. Zhang, G. H. Chen, “The analysis of domino effect impact probability triggered by fragments”, Safety Science, vol.47, pp.1026-1032, 2009.
[17] S. N. J. Watamaniuk, S. P. Mckee, N. M. Grzywacz, “Detecting a Trajectory Embedded in Random-direction Motion Noise”, Vision Research, vol.35, no.1, pp.65-77, 1995.
[18] J. Duan, X. C. Fu, P. D. Liu, A. Manning, “A linear chaotic quantum harmonic oscillator”, Applied Mathematics Letters, vol.12, no.1, pp.15-19, 1999.
[19] L. Tian, Z. Liu, L. Yang, “Can the linear operator in physics cause chaos?”, Communications in Nonlinear Science and Numerical Simulation, vol.2, no.2, pp.128-131, 1997.
[20] D. Guégan, “Chaos in economics and finance”, Annual Reviews in Control, vol.33, no.1, pp.89-93, 2009.
[21] S. Barton, “Chaos, Self-Organization, and Psychology”, American Psychologist, vol.49, no.1, pp.5-14, 1994.
[22] Q. Yuan, X. S. Yang, “Computer-assisted verification of chaos in the model of nuclear spin generator”, Applied Mathematics and Computation, vol.213, no.1, pp.148-152, 2009.
[23] A. L. Fradkov, R. J. Evans, “Control of chaos: Methods and applications in engineering”, Annual Reviews in Control, vol.29, no.1, pp.33-56, 2005.
[24] H. T. Yau, J. J. Yan, “Chaos synchronization of different chaotic systems subjected to input nonlinearity”, Applied Mathematics and Computation, vol.197, no.2, pp.775-788, 2008.
[25] R. N. Madan, “Chua’s Circuit: A Paradigm for Chaos”, World Scientific Publishing Company, Singapore, 1993.
[26] M. J. Ogorzalek, Z. Galias, “Characterization of chaos in Chua's oscillator in terms of unstable periodic orbits”, Journal of Circuits, Systems and Computers, vol.3, no.2, pp.411–429, 1993.
[27] J. L. Mancilla-Aguilar, R. A. García, “Input / output stability of systems with switched dynamics and outputs”, Systems & Control Letters, vol.57, no.9, pp.726-732, 2008.
[28] W. A. Zhang, L. Yu, “Stability analysis for discrete-time switched time-delay systems”, Automatica, vol.45, no.10, pp.2265-2271, 2009.
[29] J. Zhao, D. J. Hill, “Passivity and stability of switched systems: A multiple storage function method”, Systems & Control Letters, vol.57, no.2, pp.158-164, 2008.
[30] C. H. Lien, K. W. Yu, Y. J. Chung, Y. F. Lin, L. Y. Chung, J. D. Chen, “Exponential stability analysis for uncertain switched neutral systems with interval-time-varying state delay”, Nonlinear Analysis: Hybrid Systems, vol.3, no.3, pp.334-342, 2009.
[31] K. Gu, V. L. Kharitonov, J. Chen, “Stability of Time-Delay Systems”, Birkhauser, Boston, 2003.
[32] P. E. Allen, D. R. Holberg, “CMOS Analog Circuit Design”, Oxford University Press, New York, 2002.
[33] G. Ferri, N. C. Guerrini, “Low-Voltage Low-Power CMOS Current Conveyors”, Springer Netherlands, Boston, 2003.
[34] J. T. Spooner, M. Maggiore, R. Ordonez, K. M. Passino, “Stable Adaptive Control and Estimation for Nonlinear Systems : Neural and Fuzzy Approximation Techniques”, Wiley-Interscience, New York, 2002.
[35] G. Tao, “Adaptive Control Design and Analysis”, Wiley-Interscience, Hoboken, 2003.
[36] K. S. Narendra, A. M. Annaswamy, “Stable Adaptive Systems”, Prentice-Hall International, Inc., Englewood Cliffs, 1989.
[37] Z. Sun, S. S. Ge, “Switched Linear Systems – Control and Design”, Springer, London, 2005.
[38] B. L. Hao, “Chaos”, World Scientific, Singapore, 1984.