本論文主要乃探討幾種不同類型的非線性動態系統的穩定性、穩定化及同步問題。首先，考慮某一類型非線性類神經系統，包括多個延遲及區間時間延遲系統，利用李亞普諾夫穩定性準則、萊布尼茲-牛頓準則及線性矩陣不等式最佳化技巧從事穩定性分析，提出較不保守時間相關之穩定性判斷準則。第二部份，利用高木-菅野模糊模式探討具時變延遲類神經及不確定系統之穩定性與穩定化問題。第三部份，提出兩類具雜訊干擾的非線性系統的強健控制器設計。最後，考慮具/不具多重時間延遲或時變延遲非線性混沌同步問題。本論文將所獲之結果與其他文獻的成果相比較，並說明改進之處。

In this dissertation, the stability, stabilization, and synchronization problems of the various nonlinear dynamical systems are investigated. Firstly, the stability analysis of various classes of nonlinear neural networks with multiple delays and/or interval time-varying delays, are considered by Lyapunov stability theory, Leibniz-Newton formula, and linear matrix inequality (LMI) technique approach. The less conservative delay-dependent stability criteria are derived. Secondly, we propose stability and stabilization problems of neural networks and uncertain nonlinear systems with time-varying delays via Takagi-Sugeno (T-S) fuzzy model approach. Thirdly, the robust controller design for two classes of nonlinear systems with noise perturbation (disturbance) is developed. Finally, the synchronization problems of nonlinear chaotic systems with/without multiple delays or time-varying delays are investigated. The significant improvements of our results over the recent existing results are observed if the comparisons are possible. Some illustrative examples are given in appropriate places to demonstrate the effectiveness of our main results.

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