分数阶时滞切换线性系统的稳定性研究  

Stability Study of Time-Lagged Switched Linear System of Fractional Order

作　　者：田吉 龙飞[2] 徐鹏 TIAN Ji;LONG Fei;XU Peng(College of Electrical Engineering,Guizhou University,Guiyang 550025,China;College of Artificial Intelligence and Electrical Engineering,Guizhou Institute of Technology,Guiyang 550003,China)

机构地区：[1]贵州大学电气工程学院,贵州贵阳550025 [2]贵州理工学院人工智能与电气工程学院,贵州贵阳550003

出　　处：《自动化仪表》2024年第6期11-16,21,共7页Process Automation Instrumentation

基　　金：国家自然科学基金资助项目(61813006、61973329);贵州省基础研究计划重点基金资助项目(20191416);贵州省高等学校科研创新团队基金资助项目(2022033)。

摘　　要：为了更好地了解系统时滞对分数阶切换系统稳定性的影响,研究了Caputo分数阶时滞切换线性系统的有限时间稳定性。首先,通过求解给定的分数阶时滞线性系统,导出了Lyapunov函数沿分数阶线性时滞系统的Caputo分数阶导数满足的不等式条件。其次,基于该不等式条件和Heaviside阶跃函数的性质,得到了具有Caputo分数阶导数的分段定义微分函数的等价解;通过导出的引理,得到了分数阶时滞线性切换系统有限时间稳定性的充分条件。最后,通过两个算例验证了所提方法的有效性。利用Heaviside阶跃函数得到的分段定义分数阶微分不等式的等价解,有效地克服了现有研究分数阶切换时滞系统稳定性问题中存在的忽略分数阶算子的记忆性缺陷。The finite-time stability of Caputo fractional order time-lagged switching linear systems are investigated to better understand the effect of systematic time-lagged on the stability of fractional order switching systems.Firstly,by solving the given fractional order time-lagged linear system,the inequality condition satisfied by the Caputo fractional order derivative of Lyapunov function along the fractional order linear time-lagged system is derived.Secondly,based on this inequality condition and the properties of the Heaviside step function,the equivalent solution of the segmentally defined differential function with Caputo fractional order derivatives is obtained;by means of the derived lemma,a sufficient condition for the finite-time stability of the fractional order time-lagged linear switching system is obtained.Finally,the validity of the proposed method is verfied by two arithmetic examples.By utilizing the Heaviside step function,the obtained equivalent solutions of segmentally defined fractional order calculus inequalities effectively overcome the memory defects of neglecting fractional order operators in the existing study of the stability problems of fractional order switching time-lagged systems.

关 键 词：分数阶微积分 切换线性系统 时滞 Caputo分数阶 有限时间稳定性 LYAPUNOV函数 分段定义微分函数 

分 类 号：TH701[机械工程—仪器科学与技术]