摘要
研究一类三概率区间分布时滞网络控制系统的稳定性问题。假设已知时滞在3个区间上的概率分布,首先,引入2个服从伯努利分布的随机变量来表征时滞在3个区间上的概率分布,并建立一个具有三概率区间分布时滞的系统模型;其次,在构造Lyapunov-Krasovskii泛函时,引入增广矩阵和三重四重积分项,更好地利用了系统的时滞信息;接着,运用Wirtinger积分不等式和凸组合相结合的方法处理L-K泛函中二重积分求导产生的积分项,使用Jensen不等式分别处理三重积分以及四重积分求导产生的积分项,并以线性矩阵不等式的形式给出使系统稳定的保守性较小的充分条件;最后,通过数例验证了该稳定性准则的有效性。
The stability of a class of network control systems with a three-probability-interval distributed time-delay is studied.Firstly,the probability distribution of the time delay in the three intervals is assumed to be known,two random variables that obey the Bernoulli distribution are introduced to characterize the probability of the time delay in the three intervals,and a three-interval delay system model is established.Secondly,to further utilize the time-delay information of the system,an augmented matrix and triple integral term and quadruple integral term are introduced when constructing the Lyapunov-Krasovskii(L-K)functional.Then,using the method of combining Wirtinger integral inequality and convex combination to process the integral term from the double integral derivation in the L-K functional,and using Jensen's inequality to process the integral term from the triple and quadruple integral derivation in the L-K functional,a less conservative stability criterion is given by a sufficient condition in the form of linear matrix inequalities.Finally,the validity of the stability criterion is verified by an example.
作者
戎佳豪
姜偕富
张镇佳
赵冰
RONG Jiahao;JIANG Xiefu;ZHANG Zhenjia;ZHAO Bing(School of Automation,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)
出处
《杭州电子科技大学学报（自然科学版）》
2022年第5期53-59,97,共8页
Journal of Hangzhou Dianzi University：Natural Sciences
基金
国家自然科学基金资助项目(61673148)。
关键词
概率区间分布时滞
L-K泛函
线性矩阵不等式
稳定性准则
probability interval distributed time delay
L-K functional
linear matrix inequality
stability criterion
