線性時變時滯系統穩定性與穩定化條件的新分析結果

New Stability and Stabilization Criteria for Linear Systems with Retarded Time-Varying Delay

徐嘉駿(Jia-Jiun Hsu)

指導教授 ： 練光祐

國立臺北科技大學/電資學院/電機工程系研究所/碩士(2013年)

https://doi.org/10.6841/NTUT.2013.00298

摘要

本論文旨在說明滯後型時變時滯線性系統的穩定性分析，主要基於Lyapunov定理與線性矩陣不等式的數學方法來探討穩定性與穩定化的條件。藉由建立一個新穎的增廣型Lyapunov泛函，其中包含了雙重積分項、三重積分項和一個帶有高次方純量的二次式。在推導過程中，我們使用了自由權重矩陣、詹森不等式和其延伸的引理等有效技巧來盡量減少穩定條件的保守度，時滯相關的穩定性條件最終皆以表示成線性矩陣不等式的形式。此外，我們利用這個穩定條件延伸至多面體不確定性系統進而推導出一個強健穩定性條件。最後，從條件中也可以設計出可以使系統穩定的狀態回授控制器。由數值範例可以來證實本論文所提出的方法確實改善以往文獻中的結果。

關鍵字

時變時滯 ； 穩定性 ； 線性矩陣不等式 ； 多面體型不確定性

並列摘要

This thesis considers the stability of linear systems with retarded time-varying delay. It is mainly based on Lyapunov-Krasovskii theory and linear matrix inequality (LMI) methodology to investigate the stability and stabilization criteria. By constructing a new augmented Lyapunov functional which contains double-integral terms, a triple-integral term and a higher degree scalar quadratic function, a delay-dependent stability criterion is presented in an LMI form. In derivation process, we use some effective techniques like free-weighting matrix approach, Jensen inequality and its extended lemma to reduce the conservatism of the stability criteria. Moreover, we make this criterion extend to the polytopic uncertainty system and then propose a robust stability criterion. Finally, the stability criterion is also used to design a stabilizing state-feedback controller. Numerical examples are given to show that our results achieve by far the best result in the literatures.

並列關鍵字

Time-varying Delay ； Stability ； Linear Matrix Inequality (LMI) ； Polytopic Uncertainty

參考文獻

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