摘要
针对一类具有Markov切换和时变时滞脉冲随机系统,利用Lyapunov–Krasovskii(L–K)泛函法和平均脉冲区间条件建立系统均方有限时间稳定的相关性准则。利用广义伊藤公式求出L–K泛函关于时间的导数,根据积分不等式对求出的L–K泛函导数进行放缩,降低判据的保守性;结合平均脉冲区间条件约束均匀时间间隔内脉冲发生次数,得到以线性矩阵不等式(LMI)形式的时滞相关稳定性判据,进一步降低判据的保守性;设计使系统满足有限时间稳定的状态反馈控制器,且给出实例进行验证。结果表明:本文建立的相关性准则,通过选取模态相关的泛函且利用平均脉冲区间条件,可进一步降低判据的保守性。
For a class of impulsive stochastic systems with Markov switch and time-varying delay,the correlation criterion of mean-square finite-time stability of the system was established by using Lyapunov–Krasovskii(L–K)functional method and average impulsive interval condition.The derivative of L–K functional about time was obtained by generalized Ito’s formula,and the derivative of L–K functional was scaled according to integral inequality to reduce the conservatism of the criterion.Combining with the condition of average impulsive interval to constrain the number of impulses in a uniform time interval,a delay-dependent stability criterion in the form of linear matrix inequality(LMI)was obtained to further reduce the conservatism of the criterion.A state feedback controller was designed to make the system meet the finite time stability,and an example was given to verify it.The results show that the correlation criterion established in this paper can further reduce the conservatism of the criterion by selecting the functional of modal correlation and using the condition of average impulsive interval.
作者
尹浩
姚凤麒
王国庆
YIN Hao;YAO Fengqi;WANG Guoqing(School of Electrical&Information Engineering,Anhui University of Technology,Maanshan 243032,China)
出处
《安徽工业大学学报(自然科学版)》
CAS
2024年第2期182-188,共7页
Journal of Anhui University of Technology(Natural Science)
基金
安徽省高校自然科学基金项目(2022AH050108)。