本文選題：廣義時變系統(tǒng)　切入點：矩陣微分不等式　出處：《沈陽工業(yè)大學》2015年碩士論文　論文類型：學位論文

【摘要】：現(xiàn)代科技、社會科學各個領域的實際問題中往往會存在瞬時突變現(xiàn)象，這種現(xiàn)象不能用單純的微分或差分方程來表示，而用基于跳變的微分方程描述更加合適�；谔兊奈⒎址匠棠軌虺浞值目紤]到瞬間突發(fā)現(xiàn)象對系統(tǒng)狀態(tài)的影響，并且更深刻更精確的反映事物變化的規(guī)律。因此基于跳變的微分系統(tǒng)在工程實踐中具有一定的應用價值。 本文研究了基于跳變的廣義時變系統(tǒng)的時域控制問題。首先，研究了基于跳變的廣義時變系統(tǒng)的輸入輸出時域穩(wěn)定問題。基于矩陣微分不等式，對應于L2干擾輸入給出了一個上述系統(tǒng)輸入輸出時域穩(wěn)定的充分條件，并對應L干擾輸入給出了一個上述系統(tǒng)輸入輸出時域穩(wěn)定的充分條件。這樣的條件要求矩陣微分不等式解的存在性。接下來根據(jù)給出的充分條件設計了控制器，使得閉環(huán)系統(tǒng)輸入輸出時域穩(wěn)定。本文的結(jié)果對于一般情況下的廣義時變系統(tǒng)是同樣適用的。對于廣義條件的非嚴格矩陣不等式給出了一種化簡的方法將其轉(zhuǎn)化為嚴格的矩陣不等式，對于時變的矩陣不等式給出了一種分段線性化的算法使得可以應用Matlab LMIs工具箱對其求解。最后，我們給出了兩個算例來驗證結(jié)果的有效性。 接下來，研究了帶有時變不確定性的基于跳變的廣義時變系統(tǒng)的時域H∞控制問題，給出了時域H∞控制的概念。首先給出了上述系統(tǒng)時域有界的充分條件，，然后將結(jié)論推廣到時域H∞的情形并給出了一個充分條件�；诮o出的充分條件設計了控制器使得閉環(huán)系統(tǒng)時域有界且滿足L2增益。所有的條件都是以矩陣不等式和微分矩陣不等式的形式給出的，對于廣義條件的非嚴格矩陣不等式給出了一種化簡的方法將其轉(zhuǎn)化為嚴格的矩陣不等式。對于時變的矩陣不等式給出了一種分段線性化的算法使得可以應用Matlab LMIs工具箱對其求解。最后給出了一個數(shù)值算例驗證了結(jié)論的有效性。
[Abstract]:In modern science and technology, social science and social science, there is often a transient abrupt change in practical problems, which can not be expressed by a simple differential or difference equation. It is more suitable to describe the differential equation based on jump. The differential equation based on jump can fully take into account the effect of the instantaneous burst phenomenon on the system state. Therefore, the differential system based on jump has certain application value in engineering practice. In this paper, the time-domain control problem of generalized time-varying systems based on jump is studied. Firstly, the input and output time-domain stability of generalized time-varying systems based on jump is studied. Corresponding to the L2 interference input, a sufficient condition for the time-domain stability of the input and output of the system mentioned above is given. A sufficient condition for the time-domain stability of the input and output of the system mentioned above is given, which requires the existence of the solution of the matrix differential inequality. Then, the controller is designed according to the sufficient conditions given. The results obtained in this paper are also applicable to generalized time-varying systems under general conditions. A simplified method is given for the non-strict matrix inequalities with generalized conditions. For strict matrix inequalities, A piecewise linearization algorithm is presented for time-varying matrix inequalities, which can be solved by using the Matlab LMIs toolbox. Finally, two examples are given to verify the validity of the results. Then, the time-domain H _ 鈭

本文編號：1620507