【摘要】：本文主要探究了幾類(lèi)2-D離散模糊系統(tǒng)的穩(wěn)定問(wèn)題,對(duì)系統(tǒng)的穩(wěn)定性進(jìn)行了分析,并設(shè)計(jì)了針對(duì)不同系統(tǒng)的狀態(tài)反饋控制器和輸出反饋控制器。由于2-D離散模糊系統(tǒng)依賴兩個(gè)變量變化,若直接采用處理1-D系統(tǒng)的方法,將不能得到有效的結(jié)果,而對(duì)其較好的處理方法就是在兩個(gè)變量變化的方向上分別選取不同的Lyapunov函數(shù)。其主要內(nèi)容可分為下面三個(gè)部分:第一部分主要對(duì)一類(lèi)2-D離散模糊系統(tǒng),設(shè)計(jì)了狀態(tài)反饋控制器。該部分所采用的不確定性為帶有線性分式不確定情況,這包含了范數(shù)有界不確定性,具有更一般的意義。通過(guò)引入一個(gè)自由權(quán)矩陣,采用并行分布補(bǔ)償方法,將當(dāng)前狀態(tài)和控制輸入看作兩個(gè)獨(dú)立變量,設(shè)計(jì)出的狀態(tài)反饋控制器能夠使得該類(lèi)系統(tǒng)漸近穩(wěn)定。最后利用凸優(yōu)化方法得到了狀態(tài)反饋控制器增益。第二部分主要對(duì)一類(lèi)2-D離散模糊系統(tǒng),設(shè)計(jì)了輸出反饋控制器和H_∞輸出反饋控制。輸出反饋控制作為控制系統(tǒng)設(shè)計(jì)中的一種重要方法在該部分得到了充分的研究,不僅考慮了確定2-D系統(tǒng)的輸出反饋控制和具有H_∞性能指標(biāo)的輸出反饋控制,還考慮了包括不確定2-D系統(tǒng)在內(nèi)的輸出反饋控制和H_∞輸出反饋控制。通過(guò)對(duì)系統(tǒng)矩陣進(jìn)行奇異值分解,有效地解決了反饋增益矩陣與系統(tǒng)矩陣間的耦合關(guān)系,使得輸出反饋控制器增益可以通過(guò)求解一系列矩陣不等式而得到。在H_∞性能作為衡量一個(gè)系統(tǒng)抑制干擾的重要指標(biāo)情況下,本章中所設(shè)計(jì)的H_∞輸出反饋控制器能夠?qū)崿F(xiàn)系統(tǒng)對(duì)干擾的抑制。第三部分主要針對(duì)一類(lèi)2-D離散隨機(jī)模糊系統(tǒng),設(shè)計(jì)了H_∞狀態(tài)反饋控制器。首先,2-D離散隨機(jī)模糊系統(tǒng)是把FM第二模型中的系統(tǒng)矩陣擴(kuò)展成隨機(jī)矩陣而得到的,隨機(jī)矩陣中新添加的項(xiàng)可以看成是對(duì)系統(tǒng)矩陣的隨機(jī)擾動(dòng)。其次,利用Lyapunov函數(shù)方法,引入自由權(quán)矩陣,建立了滿足給定性能指標(biāo)并使得系統(tǒng)均方漸近穩(wěn)定的充分條件。最后,通過(guò)仿真例子證明了所得結(jié)果的正確性。
[Abstract]:In this paper, the stability problems of 2-D discrete fuzzy systems are discussed, the stability of the systems is analyzed, and the state feedback controllers and output feedback controllers for different systems are designed. Because 2-D discrete fuzzy system depends on two variables, if the method of dealing with 1-D system is adopted directly, the effective result can not be obtained, and the better way to deal with it is to select different Lyapunov functions in the direction of the change of the two variables. The main contents can be divided into the following three parts: in the first part, a state feedback controller is designed for a class of 2-D discrete fuzzy systems. The uncertainty used in this part is the uncertainty with linear fractions which contains norm-bounded uncertainties and has a more general meaning. By introducing a free right matrix and using a parallel distributed compensation method, the current state and the control input are regarded as two independent variables. The designed state feedback controller can make the system asymptotically stable. Finally, the state feedback controller gain is obtained by convex optimization method. In the second part, the output feedback controller and H _ 鈭，

本文編號(hào)：2190880