山东大学学报（工学版）
山東大學學報（工學版）
산동대학학보（공학판）
JOURNAL OF SHANDONG UNIVERSITY(ENGINEERING SCIENCE)
2015年
1期
54-63
,共10页
随机系统%鲁棒随机稳定%线性结构不确定性%多时滞%李雅普诺夫函数%LMI
隨機繫統%魯棒隨機穩定%線性結構不確定性%多時滯%李雅普諾伕函數%LMI
수궤계통%로봉수궤은정%선성결구불학정성%다시체%리아보낙부함수%LMI
stochastic system%robust stochastical stability%linear fractional uncertainties%multiple delays%Lyapunov-Krasovskii function%LMI
研究了一类不确定随机多时滞系统的鲁棒随机稳定性问题，其中系统不确定参数满足线性分式结构。首先，将倒数凸方法加以推广，得到一个新的积分不等式引理；然后，充分考虑时滞区间上下限关系，构造了多时滞区间相关的李雅普诺夫函数，并在新的积分不等式方法下，得到具有更小保守性和较少自由变量的时滞相关稳定性条件；最后，给出一些数值仿真实例，验证了所提方法的有效性。
研究瞭一類不確定隨機多時滯繫統的魯棒隨機穩定性問題，其中繫統不確定參數滿足線性分式結構。首先，將倒數凸方法加以推廣，得到一箇新的積分不等式引理；然後，充分攷慮時滯區間上下限關繫，構造瞭多時滯區間相關的李雅普諾伕函數，併在新的積分不等式方法下，得到具有更小保守性和較少自由變量的時滯相關穩定性條件；最後，給齣一些數值倣真實例，驗證瞭所提方法的有效性。
연구료일류불학정수궤다시체계통적로봉수궤은정성문제，기중계통불학정삼수만족선성분식결구。수선，장도수철방법가이추엄，득도일개신적적분불등식인리；연후，충분고필시체구간상하한관계，구조료다시체구간상관적리아보낙부함수，병재신적적분불등식방법하，득도구유경소보수성화교소자유변량적시체상관은정성조건；최후，급출일사수치방진실례，험증료소제방법적유효성。
The problem of robust stochastic stability for a class of uncertain stochastic systems with multiple delays was investigated in this paper.The uncertainties were in linear fractional form.Firstly,a new integral inequlity lemma was derived by extending the reciprocally convex approach.Then,based on a multiple delay-interval dependent Lyapunov-Krasovskii constructed by fully considering the relationship between upper and lower time delay interval and the new in-tegral inequlity approach,some novel delay-dependent stability criteria with less conservatism and less free weighting matrices were obtained.At last,some numerical examples were given to show the effectiveness of the proposed results.
