Lyapunov functions for nabla discrete fractional order systems
Lyapunov functions for nabla discrete fractional order systems
复制标题
nabla 离散分数阶系统的 Lyapunov 函数
DOI：
10.1016/j.isatra.2018.12.016
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发表时间：
2019
期刊：
影响因子：
7.3
通讯作者：
Yong Wang
中科院分区：
文献类型：
--
作者：
Yiheng Wei;Yuquan Chen;Tianyu Liu;Yong Wang
研究了与Riemann-Liouville、Caputo和Grünwald-Letnikov定义相关的李雅普诺夫函数的分数阶差分.首先介绍了构造李雅普诺夫函数的一种新方法，然后对每个定义导出了五个不等式。利用所建立的不等式，得到了nabla离散分数阶非线性系统渐近稳定的充分条件。最后，通过三个算例验证了理论结果的有效性和可行性。
This paper focuses on the fractional difference of Lyapunov functions related to Riemann–Liouville, Caputo and Grünwald–Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results.