本文關(guān)鍵詞：奇異攝動系統(tǒng)的魯棒穩(wěn)定性分析與反饋控制　出處：《華東師范大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 奇攝動系統(tǒng) 魯棒穩(wěn)定 輸入狀態(tài)穩(wěn)定 輸出反饋 線性矩陣不等式 馬爾克夫跳變系統(tǒng) H_∞控制

【摘要】：兩時標(biāo)結(jié)構(gòu)是奇異攝動系統(tǒng)或奇攝動系統(tǒng)固有的特性,這個特性通常會導(dǎo)致系統(tǒng)階數(shù)的增加和剛性問題的產(chǎn)生.從而大大增加了對系統(tǒng)分析和控制的復(fù)雜性.為了克服上述問題的產(chǎn)生,奇攝動方法應(yīng)運(yùn)而生.在過去的40年,奇攝動方法獲得了廣泛的認(rèn)可并在控制領(lǐng)域快速發(fā)展.目前,有關(guān)連續(xù)時間和離散時間兩種情形下奇攝動系統(tǒng)理論的研究均己取得了很大的進(jìn)展.本論文在深入研究奇攝動系統(tǒng)的魯棒穩(wěn)定以及反饋控制問題的基礎(chǔ)之上,獲得了一些新的結(jié)果,特別是離散奇攝動系統(tǒng)的研究,主要研究內(nèi)容如下：(1)研究了連續(xù)和離散時間兩種情形下具有非線性擾動的奇攝動系統(tǒng)的魯棒穩(wěn)定性與反饋控制問題.利用不動點定理和線性矩陣不等式技巧,給出了系統(tǒng)存在孤立根的充分條件.在此基礎(chǔ)上,利用兩時標(biāo)方法分別獲得了快慢子系統(tǒng)輸入狀態(tài)穩(wěn)定的充分條件,利用給合方法的技巧,在系統(tǒng)內(nèi)部穩(wěn)定的條件下,進(jìn)一步給出了全階系統(tǒng)輸入狀態(tài)穩(wěn)定的充分條件.同時,當(dāng)系統(tǒng)內(nèi)部不穩(wěn)定時,給出了系統(tǒng)輸入狀態(tài)穩(wěn)定反饋控制律的設(shè)計.(2)研究了離散時間奇攝動系統(tǒng)的H∞分析和控制問題.在時標(biāo)分解的基礎(chǔ)上,通過分析相應(yīng)的快和慢子系統(tǒng),首次給出了全階系統(tǒng)具有給定的H∞性能指標(biāo)的充分條件.同時,給出了閉環(huán)系統(tǒng)具有給定H∞性能指標(biāo)的狀態(tài)反饋控制律設(shè)計.(3)利用奇攝動方法,研究了離散時間奇攝動系統(tǒng)的嚴(yán)真動態(tài)輸出的反饋控制問題.利用線性矩陣不等式技巧,分別對快和慢子系統(tǒng)的動態(tài)輸出反饋控制器進(jìn)行了設(shè)計,最后利用組合技巧,復(fù)合獲得到原系統(tǒng)的動態(tài)輸出反饋控制.結(jié)果顯示,在復(fù)合動態(tài)輸出反饋控制律作用下,當(dāng)小參數(shù)充分小時,原系統(tǒng)是鎮(zhèn)定的.(4)研究了離散時間奇攝動系統(tǒng)非嚴(yán)真的動態(tài)輸出反饋控制問題.通過建立輔助系統(tǒng)的方法,將非嚴(yán)真的動態(tài)輸出反饋控制問題轉(zhuǎn)化為分別同時設(shè)計輔助系統(tǒng)的嚴(yán)真動態(tài)輸出反饋與快子系統(tǒng)的靜態(tài)輸出反饋控制.結(jié)果顯示,所提出的設(shè)計方法能保證原系統(tǒng)是鎮(zhèn)定的.從而克服了對動態(tài)輸出反饋控制嚴(yán)真要求的限制.(5)利用線性矩陣不等式技巧,研究了馬爾克夫跳變奇攝動系統(tǒng)的H∞控制問題.給出了新的求解H∞控制器的方法.避免了求解非線性矩陣不等式和Riccati方程所帶來的困難.并在此基出上給出了求解奇攝動系統(tǒng)的最大穩(wěn)定界的方法.
[Abstract]:The structure of two timescale is the characteristic of singularly perturbed system or singularly perturbed system. This characteristic usually leads to the increase of system order and the generation of rigid problem, which greatly increases the complexity of system analysis and control. The singularly perturbed method came into being. In the past 40 years, the singularly perturbed method has been widely accepted and developed rapidly in the field of control. Great progress has been made on the theory of singularly perturbed systems in the case of continuous time and discrete time. In this paper, the robust stability and feedback control of singularly perturbed systems are studied in depth. Some new results are obtained, especially the study of discrete singularly perturbed systems. The main contents of the study are as follows:. The problem of robust stability and feedback control for singularly perturbed systems with nonlinear perturbations under both continuous and discrete-time conditions is studied. The fixed point theorem and the technique of linear matrix inequality are used. The sufficient conditions for the existence of isolated roots of the system are given. Based on this, the sufficient conditions for the stability of the input state of the fast and slow subsystems are obtained by using the two-time scale method, and the technique of the given combination method is used. Under the condition of internal stability of the system, the sufficient conditions for the stability of the input state of the full-order system are further given. At the same time, when the system is not stable inside the system. The H 鈭，

本文編號：1358882