離散時間延遲系統之穩定性分析與迴授之穩定化設計

本論文主要使用線性矩陣不等式的方法研究離散時間延遲系統。研究主題包括具有時變之狀態時間延遲的離散系統、具有時變之狀態時間延遲與非線性擾動的離散系統，及具有時變之狀態間隔時間延遲的離散系統，探討其穩定性分析與輸出迴授穩定化設計。在穩定性分析方面，本論文提出一些以線性矩陣不等式表示的穩定性準則，且在推導穩定性準則的過程中引入新的自由權重矩陣，及使用最少的不等式，儘可能不使用會產生保守性的條件。在輸出迴授控制器的設計上，本論文提出一套以線性矩陣不等式作為條件的穩定化方法，不僅可容許較大的延遲範圍使得閉迴路延遲系統穩定，對於控制器增益尚可直接求得，以對控制器增益作適當的限制，這在實際工業應用上提供設計者相當大的便利性。最後，在數值範例的測試上，本論文所提的方法不僅可以得到較為不保守的條件，甚至對於一般文獻無法討論的穩定度系統也能夠適用。

關鍵字

離散系統；時變狀態時間延遲；線性矩陣不等式；穩定性分析；輸出迴授；非線性擾動

並列摘要

This dissertation studies discrete-time systems with a time-varying state delay via the linear matrix inequality approach. The research includes the developments of delay- dependent stability analysis and output feedback stabilization for discrete-time systems with a time-varying state delay, discrete-time systems with a time-varying state delay and nonlinear perturbations, and discrete-time systems with an interval time-varying state delay. The derivations are based on the Lyapunov method and formulated by the linear matrix inequalities, which are convenient to solve. In the development of stability condi- tions, new free-weighting matrices are introduced, and the least number of inequalities are utilized, with the attempt to reduce as much conservatism as possible. In the proposed novel stabilizing output feedback controller design method, the gain matrix is a direct design variable, which offers great flexibility for the design purpose. To test the derived results, many numerical examples are adopted. Comparisons with results by existing methods indeed show that the proposed method is less conservative for the examples.

並列關鍵字

discrete-time system ； time-varying state delay ； linear matrix inequality ； stability analysis ； output-feedback ； l nonlinear perturbation

參考文獻

[1]J. K. Hale and S. M. Verduyn Luned, Introduction to Functional Differential Equations, Springer, New York, NY, 1993.

[2]V. B. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Dordrecht, Kluwer Academic Publishers, 1999.

[3]M. Malek-Zavarei and M. Jamshidi, Time-Delay Systems, Analysis, Optimization and Application, North-Holland Systems and Control Series, 1987.

[4]H. Gorecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, John Wiley and Sons, Warszawa, 1989.

[5]M. S. Mahmoud, Robust Control and Filtering for Time-delay Systems, Marcel-Dekker, New York, NY, 2000.

國際替代計量

離散時間延遲系統之穩定性分析與迴授之穩定化設計

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