Open AccessLyapunov functions for fractional order h-difference systems
Author(s) -
Xiang Liu,
Baoguo Jia,
Lynn Erbe,
Allan Peterson
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2104155l
Subject(s) - mathematics , lyapunov function , order (exchange) , polynomial , quadratic equation , lyapunov equation , integer (computer science) , lyapunov exponent , stability (learning theory) , fractional calculus , lyapunov redesign , fractional order system , pure mathematics , mathematical analysis , nonlinear system , physics , geometry , finance , quantum mechanics , machine learning , computer science , economics , programming language
This paper presents some new propositions related to the fractional order h-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order h-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.