摘要
对一个具有外部扰动的系统而言,通常想知道这个系统的状态量在给定的初值条件下,在多长的时间段内不会超过一个给定的界。对于非线性系统而言,由于其研究方法的局限性,相关的研究成果不像线性系统的丰富,相应的研究通常都用到诸如线性化、Lipschitz条件等。这些条件对方程的要求较高,或舍弃的信息量较大。根据有限时间稳定性定义的特点,提出了一个比较简单的条件来研究一类非线性系统的有限时间稳定性和有界性问题。在给定的条件下,得到了这类非线性系统的有限时间稳定性及有限时间有界性的充分条件,为了方便进行模拟,也用矩阵不等式给出了相应的结果。最后通过数字仿真研究了这些结果的可行性。
For a system with external disturbances,we want to know how long the state of this system will not exceed a given bound under a given initial value conditions.For nonlinear systems,due to the limitations of its research methods,the relevant research results are not as rich as that of the linear system.The research methods usually use such as linearization,Lipschitz condition and so on.According to the characteristics of the definition of finite-time stability and finite-time boundedness,a condition is proposed to study the finite time stability and boundedness of a class of nonlinear systems.Under the given condition,sufficient conditions for the finite-time stability and finite-time boundedness of this kind of nonlinear system are obtained.In order to facilitate the simulation,the corresponding results are also given by using linear matrix inequality.Finally,the feasibility of these results is studied by digital simulation.
作者
姚玉武
闫晓辉
胡秀林
YAO Yu-wu;YAN Xiao-hui;HU Xiu-lin(School of Artificial Intelligence and Big Data,Hefei University,Hefei 230601,China;Sino-German Institute of Applied Mathematics,Hefei University,Hefei 230601,China)
出处
《合肥学院学报（综合版）》
2020年第2期1-6,共6页
Journal of Hefei University：Comprehensive ED
基金
安徽省高校自然科学研究重点项目(KJ2018A0565)
安徽省自然科学基金(1908085QF290)
合肥学院科研发展基金重大项目(18ZR11ZDA)资助。
关键词
非线性系统
离散系统
有限时间稳定性
有限时间有界性
nonlinear system
discrete-time systems
finite-time stability
finite-time boundedness
