Lyapunov functions for fractional order h-difference systems
Abstract
This paper presents some new propositions related to the fractional order -difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order -difference systems, by means of the discrete fractional Lyapunov direct method, using general quadratic Lyapunov functions, and polynomial Lyapunov functions of any positive integer order, respectively. Some examples are given to illustrate these results.
Cite
@article{arxiv.2006.08237,
title = {Lyapunov functions for fractional order h-difference systems},
author = {Xiang Liu and Baoguo Jia and Lynn Erbe and Allan Peterson},
journal= {arXiv preprint arXiv:2006.08237},
year = {2020}
}
Comments
This paper proves the stability of fractional order h-difference systems using Lyapunov functions. Several interesting lemmas are proved. The questions posed are identifiable and understood, the conditions are well controlled. The paper has original value and what extends is useful for the large area of researchers that study fractional order equations and systems