Lyapunov functions for nabla discrete fractional order systems
Dynamical Systems
2022-12-07 v2 Signal Processing
Abstract
This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-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.
Cite
@article{arxiv.1812.11368,
title = {Lyapunov functions for nabla discrete fractional order systems},
author = {Yiheng Wei and Yuquan Chen and Tianyu Liu and Yong Wang},
journal= {arXiv preprint arXiv:1812.11368},
year = {2022}
}
Comments
21 pages, 3 figures