Lyapunov functions for fractional-order nonlinear systems with Atangana-Baleanu derivative of Riemann-Liouville type

abstract

• Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order 0<<1 modeled by the AtanganaBaleanu derivative of RiemannLiouville type (ABR), which allows consistent modeling of a large class of physical systems with complex dynamics. The main contribution of the paper consists of some novel inequalities for the AtanganaBaleanu derivative of the RiemannLiouville type. Furthermore, the proposed study allows considering both quadratic and convex Lyapunov functions to analyze stability in ABR systems by applying the Direct Lyapunov Method.

authors

• Munoz Vazquez, Aldo Jonathan

published proceedings

• MATHEMATICAL METHODS IN THE APPLIED SCIENCES

author list (cited authors)

• Martinez-Fuentes, O., Fernandez-Anaya, G., & Jonathan Munoz-Vazquez, A.

complete list of authors

• Martinez-Fuentes, Oscar||Fernandez-Anaya, Guillermo||Jonathan Munoz-Vazquez, Aldo

publisher

• Wiley  Publisher

published in

• Mathematical Methods in the Applied Sciences  Journal

keywords

• Asymptotic Stability
• Atangana-baleanu Derivative Of Riemann-liouville Type
• Lyapunov Direct Method
• Mittag-leffler Nonsingular Kernel
• Mittag-leffler Stability

Digital Object Identifier (DOI)

• 10.1002/mma.7690

start page

• 14206

end page

• 14216

volume

• 44

issue

• 18