在本篇論文中，首先提出實用指數穩定化的觀念，緊接著針對一類超混沌控制系統，結合類里亞普若夫理論及微分積分不等式，提出兩套線性控制器，促使上述系統達成全域指數穩定的標的。由於所設計的控制器為線性控制器，故其可經由電子電路來實現。另一方面，吾人擬提出ε-δ 同步化的概念﹝註：ε為收歛半徑，δ 為收斂速率﹞，並針對一類具混合式不確定項之主僕控制系統，利用微分及積分不等式，設計一套保證上述不確定主僕系統達成ε-δ 同步化之新型追蹤控制器。此控制器不僅指數收斂速率及收斂半徑可事先安排，亦能克服系統外在之混合式不確定項。最後將提供多個數值範例，來驗證及說明主要定理的正確性。

In this thesis, the concept of practical exponential stabilizability is introduced and the stabilization for a class of hyperchaotic systems is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, two linear feedback controllers are proposed to realize the global exponential stabilization of such systems. Besides, the proposed control can be directly and efficiently realized by easy-implemented electronic circuits. On the other hands, the concept of ε-δ synchronization is introduced and the ε-δ synchronization for a class of uncertain master-slave systems with mixed uncertainties is investigated. Based on the differential and integral inequalities methodology, a tracking control is proposed to realize the ε-δ synchronization for such uncertain systems. Not only the guaranteed exponential decay rate and convergence radius can be pre-specified, but also the mixed uncertainties can be simultaneously conquered by the proposed control.Finally, numerical simulations will be given to demonstrate the feasibility and effectiveness of the obtained results.

中文摘要 I
英文摘要 II
目錄 III
圖目錄 IV
第一章 導論 1
第二章 超混沌系統之線性控制器設計 3
第三章 不確定超混沌主僕系統之追蹤控制器的設計 20
第四章 結論及未來研究方向 33
附錄 34
參考文獻 53
已刊登的文章 60

[1] M. M. Aziz, S. F. AL-Azzawi, Anti-synchronization of nonlinear dynamical systems based on Gardano’s method, Optik-International Journal for Light and Electron Optics, Volume 134, April 2017, Pages 109-120.
[2] H. Tirandaz, A. Hajipour, Adaptive synchronization and anti-synchronization of TSUCS and Lü unified chaotic systems with unknown parameters,Optik-International Journal for Light and Electron Optics, Volume 130,February 2017, Pages 543-549.
[3] D. S. Laiphrakpam, M. S. Khumanthem, Cryptanalysis of symmetric key image encryption using chaotic Rossler system, Optik-International Journal for Light and Electron Optics, Volume 135, April 2017, Pages 200-209.
[4] J. Yu, J. Lei, L. Wang, Backstepping synchronization of chaotic system based on equivalent transfer function method, Optik-International Journal for Light and Electron Optics, Volume 130, February 2017, Pages 900-913.
[5] Z. Wang, C. Volos, S. T. Kingni, A. T. Azar, V. T. Pham, Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity, Optik-International
Journal for Light and Electron Optics, Volume 131, February 2017, Pages 1071-1078.
[6] J. Yu, J. Lei, Synchronization of chaotic system with adaptive transfer function sliding mode method, Optik-International Journal for Light and Electron Optics,
Volume 132, March 2017, Pages 299-319.
[7] J. Yu, J. Le, D. Liu, Synchronization of chaotic system with adaptive transfer function sliding mode method, Optik-International Journal for Light and
Electron Optics, Volume 130, February 2017, Pages 1053-1072.
[8] C. L. Li, J. B. Xiong, A simple chaotic system with non-hyperbolic equilibria,Optik-International Journal for Light and Electron Optics, Volume 128, January 2017, Pages 42-49.
[9] B. Wang, S. M. Zhong, Observer-based control on a chaotic system with unknowns and uncertainties, Optik-International Journal for Light and Electron Optics, Volume 137, May 2017, Pages 167-174.
[10] V. T. Pham, S. Jafari, C. Volos, T. Gotthans, D. V. Hoang, A chaotic system with rounded square equilibrium and with no-equilibrium, Optik-InternationalJournal for Light and Electron Optics, Volume 130, February 2017, Pages 365-371.
[11] Z. Li, J. Tang, Generalized binary function projective synchronization of
chaotic systems with unknown parameters, Optik-International Journal for Light and Electron Optics, Volume 137, May 2017, Pages 101-107.
[12] F. Yu, L. Gao, K. Gu, B. Yin, Z. Zhou, A fully qualified four-wing four-dimensional autonomous chaotic system and its synchronization, Optik -
International Journal for Light and Electron Optics, Volume 131, February 2017, Pages 79-88.
[13] H. Liu, A. Kadir, X. Sun, Chaos-based fast colour image encryption scheme with true random number keys from environmental noise, IET Image Processing,
Year: 2017, Volume: 11, Issue: 5, Pages: 324-332.
[14] J. Hou, R. Xi, P. Liu, T. Liu, The switching fractional order chaotic system and its application to image encryption, IEEE/CAA Journal of Automatica Sinica,
Year: 2017, Volume: 4, Issue: 2, Pages: 381-388.
[15] W. Gu, Y. Yu, W. Hu, Artificial bee colony algorithmbased parameter estimation of fractional-order chaotic system with time delay, IEEE/CAA Journal of Automatica Sinica, Year: 2017, Volume: 4, Issue: 1, Pages: 107-113.
[16] H. Peng, Y. Tian, J. Kurths, L Li, Y. Yang, D. Wang, Secure and energy-efficient data transmission system based on chaotic compressive sensing in body-to-body networks, IEEE Transactions on Biomedical Circuits and
Systems, Year: 2017, Volume: 11, Issue: 3, Pages: 558-573.
[17] J. H. P. Cruz, M. Figueroa, S. A. R. Paredes, A. L. Villa, Synchronization of chaotic Akgul system by means of feedback linearization and pole placement, IEEE Latin America Transactions, Year: 2017, Volume: 15, Issue: 2, Pages: 249-256.
[18] R. Sakthivel, S. Santra, S. M. Anthoni, V. Kuppili, Synchronisation and anti-synchronisation of chaotic systems with application to DC-DC boost converter, IET Generation, Transmission & Distribution, Year: 2017, Volume: 11, Issue: 4, Pages: 959-967.
[19] C. S. Pappu, B. C. Flores, P. S. Debroux, B. Verdin, J. Boehm, Synchronisation of bistatic radar using chaotic AM and chaos-based FM waveforms, IET Radar, Sonar & Navigation, Year: 2017, Volume: 11, Issue: 1, Pages: 90-97.
[20] C. Xue, N. Jiang, Y. Lv, K. Qiu, Secure key distribution based on dynamic chaos synchronization of cascaded semiconductor laser systems, IEEE Transactions on Communications, Year: 2017, Volume: 65, Issue: 1, Pages: 312-319.
[21] J. Ni, L. Liu, C. Liu, X. Hu, S. Li, Fast fixed-time nonsingular terminal sliding
mode control and its application to chaos suppression in power system, IEEE Transactions on Circuits and Systems II: Express Briefs, Year: 2017, Volume: 64, Issue: 2, Pages: 151-155.
[22] H. Esmaeili-Najafabadi, M. Ataei, M. F. Sabahi, Designing Sequence with minimum PSL using Chebyshev distance and its application for chaotic MIMO
radar waveform design, IEEE Transactions on Signal Processing, Year: 2017, Volume: 65, Issue: 3, Pages: 690-704.
[23] M. Chen, S. Y. Shao, P. Shi, Y. Shi, Disturbance-Observer-Based robust synchronization control for a class of fractional-order chaotic systems, IEEE Transactions on Circuits and Systems II: Express Briefs, Year: 2017, Volume: 64, Issue: 4, Pages: 417-421.
[24] X. Chen, Y. He, W. J. Lin, M. Wu, Improved synchronization of chaotic Lur ׳e systems with time delay using sampled-data control, Journal of the Franklin
Institute, Volume 354, Issue 3, February 2017, Pages 1618-1636.
[25] J. Petereit, A. Pikovsky, Chaos synchronization by nonlinear coupling, Communications in Nonlinear Science and Numerical Simulation, Volume 44, March 2017, Pages 344-351.
[26] L. Zhou, S. Liu, F. Chen, Subharmonic bifurcations and chaotic motions for a class of inverted pendulum system, Chaos, Solitons & Fractals, Volume 99, June 2017, Pages 270-277.
[27] X. Liang, G. Qi, Mechanical analysis of Chen chaotic system, Chaos, Solitons & Fractals, Volume 98, May 2017, Pages 173-177.
[28] M. R. Akbarzadeh, S. A. Hosseini, M. B. Naghibi-Sistani, Stable indirect adaptive interval type-2 fuzzy sliding-based control and synchronization of two
different chaotic systems, Applied Soft Computing, Volume 55, June 2017, Pages 576-587.
[29] X. F. Li, Y. D. Chu, A. Y. T. Leung, H. Zhang, Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls, Chaos, Solitons &
Fractals, Volume 100, July 2017, Pages 24-30.
[30] G. Xu, J. Xu, C. Xiu, F. Liu, Y. Zang, Secure communication based on the synchronous control of hysteretic chaotic neuron, Neurocomputing, Volume
227, 1 March 2017, Pages 108-112.
[31] M. J. Mahmoodabadi, R. A. Maafi, M. Taherkhorsandi, An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems, Applied Soft Computing, Volume 52, March 2017,
Pages 1191-1199.
[32] H. P. Ren, C. Bai, Q. Kong, M. S. Baptista, C. Grebogi, A chaotic spread spectrum system for underwater acoustic communication, Physica A: Statistical Mechanics and its Applications, Volume 478, 15 July 2017, Pages 77-92.