Lyapunov functions for a class of nonlinear systems using Caputo derivative
G Fernandez-Anaya, G Nava-Antonio… - … in Nonlinear Science …, 2017 - Elsevier
Communications in Nonlinear Science and Numerical Simulation, 2017•Elsevier
This paper presents an extension of recent results that allow proving the stability of Caputo
nonlinear and time-varying systems, by means of the fractional order Lyapunov direct
method, using quadratic Lyapunov functions. This article introduces a new way of building
polynomial Lyapunov functions of any positive integer order as a way of determining the
stability of a greater variety of systems when the order of the derivative is 0< α< 1. Some
examples are given to validate these results.
nonlinear and time-varying systems, by means of the fractional order Lyapunov direct
method, using quadratic Lyapunov functions. This article introduces a new way of building
polynomial Lyapunov functions of any positive integer order as a way of determining the
stability of a greater variety of systems when the order of the derivative is 0< α< 1. Some
examples are given to validate these results.
Abstract
This paper presents an extension of recent results that allow proving the stability of Caputo nonlinear and time-varying systems, by means of the fractional order Lyapunov direct method, using quadratic Lyapunov functions. This article introduces a new way of building polynomial Lyapunov functions of any positive integer order as a way of determining the stability of a greater variety of systems when the order of the derivative is 0 < α < 1. Some examples are given to validate these results.
Elsevier