脉冲依赖稳定性  

Impulse Dependent Stability

作　　者：邵林 邵汉永[2] SHAO Lin;SHAO Hanyong(College of Electronic and Information Engineering,Shandong University of Science and Technology,Qingdao 266590;Institute of Automation,Qufu Normal University,Rizhao 276826)

机构地区：[1]山东科技大学电子信息工程学院,青岛266590 [2]曲阜师范大学自动化研究所,日照276826

出　　处：《系统科学与数学》2025年第3期737-752,共16页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金面上项目(62373214)资助课题.

摘　　要：文章采用类李雅普诺夫泛函法深入研究脉冲系统的稳定性.与通常的李雅普诺夫函数相比,类李雅普诺夫泛函不要求正定也不要求连续,一般地会导致保守性较小的结果.首先,对确定系统,考虑系统当前时刻将脉冲区间划分的前后两个子区间,通过引进状态及其导数在这两个区间上的多重积分,特别是这些积分和状态、脉冲状态的交叉项,创设新的类李雅普诺夫泛函以推广现有的类李雅普诺夫函数.对类李雅普诺夫泛函导数的估计,则开发使用了系统的积分方程以充分利用系统信息,而采用了高阶积分不等式以降低估计的保守性.根据类李雅普诺夫泛函引理导出了保守性较小的稳定性判据,包括驻留时间区间、驻留时间上限和驻留时间下限稳定性判据.然后,基于这些判据研究了不确定情形,给出了新的鲁棒稳定性结果.这些稳定性和鲁棒稳定性结果具有线性矩阵不等式形式,可用Matlab中的LMI工具箱验证.最后,举例说明了所得稳定性结果具有较小的保守性.This paper is aimed at the impulse dependent stability of impulsive systems by employing a Lyapunov-like functional(LLF)which is neither necessarily positive definite nor necessarily continuous.Firstly,the stability analysis for the certain impulsive system is carried out.A new LLF is constructed by introducing multiple integrals of both state and the state derivative on the two subintervals of the impulsive interval separated by the current instant,and by including the cross products among the integral terms,the state,and the impulsive states.When estimating the derivative of the LLF,high-order integral inequalities are taken to get a tighter upper bound,and integral equations of the impulsive system are exploited to make full use of the system's information.New stability results are thus obtained for the system with the impulsive interval,maximum impulse,and minimum impulse.Secondly,based on the stability results,robust stability results are derived for impulsive systems with uncertainties.The results on both stability and robust stability are in the form of linear matrix inequalities and can be verified using the LMI toolbox in Matlab.Finally,numerical examples are listed to illustrate that the stability results have less conservatism.

关 键 词：脉冲系统 脉冲依赖稳定 鲁棒稳定 类李雅普诺夫泛函 

分 类 号：O231[理学—运筹学与控制论]