Paper Info
Title
Quadratic Lyapunov functions for stability analysis in fractional-order systems with not necessarily differentiable solutions.
Abstract
Solutions of fractional-order differintegral equations are generally not necessarily integer-order differentiable, neither in the strong nor in the weak sense, thus limiting the stability analysis in systems based on the most conventional fractional-order operators. In this paper, a consistent and well-posed definition for fractional-order systems is performed based on the study of alternative fractional-order operators that preserve the most interesting and useful properties of differintegrals, even in the case of not necessarily integer-order (weakly) differentiable functions. In addition, it is shown that these operators comply to a recently verified well-known inequality, which allows us to demonstrate Mittag-Leffler stability in a more general class of fractional-order systems, considering quadratic Lyapunov functions, by demonstrating a generalization of the Lyapunov direct method for a class of fractional-order nonlinear systems. Illustrative examples are given to highlight the feasibility of the proposed method, and a multivariable fractional integral sliding mode control application is presented.
Year
DOI
Venue
2018
10.1016/j.sysconle.2018.04.006
Systems & Control Letters
Keywords
Field
DocType
Fractional-order systems,Mittag-Leffler stability,Lyapunov direct method,Nonlinear systems
Integral sliding mode,Applied mathematics,Differintegral,Nonlinear system,Multivariable calculus,Control theory,Differentiable function,Operator (computer programming),Quadratic lyapunov function,Limiting,Mathematics
Journal
Volume
ISSN
Citations 
116
0167-6911
2
PageRank 
References 
Authors
0.39
8
4
Name
Order
Citations
PageRank
A.-J. Munoz-Vazquez1429.97
Vicente Parra-Vega218033.57
Anand Sanchez-Orta3477.64
Gerardo Romero-Galván450.87