摘 要:針對(duì)一類(lèi)線(xiàn)性不確定切換系統(tǒng),利用公共Lyapunov函數(shù)的方法,給出了當(dāng)所設(shè)計(jì)的控制器存在加性攝動(dòng)時(shí)魯棒非脆弱控制器存在的條件。該控制器能夠保證閉環(huán)切換系統(tǒng)在任意切換律下漸近穩(wěn)定。然后應(yīng)用線(xiàn)性矩陣不等式將魯棒非脆弱控制器的設(shè)計(jì)問(wèn)題轉(zhuǎn)化為一組線(xiàn)性矩陣不等式的可行解問(wèn)題,從而可借助Matlab中的LMI工具箱直接求解。最后通過(guò)仿真算例驗(yàn)證所提方法的有效性。關(guān)鍵詞:切換系統(tǒng); 公共Lyapunov函數(shù); 非脆弱控制; Matlab
中圖分類(lèi)號(hào):TN919-34文獻(xiàn)標(biāo)識(shí)碼:A
文章編號(hào):1004-373X(2010)18-0197-03
Design of Non-fragile Controller for a Class of Uncertain Switched Linear System
LI Chun-Juan,HE Yong
(Department of Electrical Engineering and Automation, Luoyang Institute of Science and Technology, Luoyang 471023, China)
Abstract: Based on the common Lyapunov function, a condition for the existence of non-fragile hybrid state-feedback controller is given according to a class of uncertain switched linear system. This controller can guarantee the linear closed-loop switched system stable asymptotically for all arbitrary uncertainties. The design of non-fragile controller can be converted into a feasible problem of certain LMI system with the linear matrix inequalities (LMI) approach. The solution of non-fragile controller can be efficiently obtained with the MATLAB toolbox. Finally, a simulation example shows the effectiveness of the proposed approaches. Keywords: switched system; common Lyapunov function; non-fragile control; Matlab
0 引 言
近年來(lái),切換系統(tǒng)以其廣泛的應(yīng)用背景和重要的理論價(jià)值受到越來(lái)越多的關(guān)注[1-2]。切換系統(tǒng)是混雜動(dòng)態(tài)系統(tǒng)中的一個(gè)重要類(lèi)型,它由一組連續(xù)微分方程描述的子系統(tǒng)以及作用在其間的切換律所構(gòu)成。這種控制系統(tǒng)在許多實(shí)際工程中經(jīng)常遇到,如電力系統(tǒng)網(wǎng)絡(luò)的切換,某些機(jī)器人控制系統(tǒng)等。目前切換系統(tǒng)的分析和設(shè)計(jì)主要集中在系統(tǒng)的穩(wěn)定性、優(yōu)化設(shè)計(jì)、魯棒性三類(lèi)問(wèn)題的單獨(dú)研究和綜合研究上[3-6]。
在實(shí)際工程中,由于硬件、軟件等原因,控制器的實(shí)現(xiàn)存在著一定的控制器參數(shù)變化,這種不確定性將導(dǎo)致閉環(huán)系統(tǒng)性能下降,甚至破壞系統(tǒng)的穩(wěn)定性。此時(shí)采用傳統(tǒng)的魯棒控制方法,將表現(xiàn)出高度的脆弱性。因此,對(duì)于非脆弱控制問(wèn)題的研究將具有重要的實(shí)際意義[7]。由于切換系統(tǒng)的連續(xù)動(dòng)態(tài)和離散動(dòng)態(tài)同時(shí)存在,對(duì)于切換系統(tǒng)的非脆弱控制相對(duì)要復(fù)雜和困難?!?br>